sta 2023 unit 3 shell notes (chapter 6 - 7)

7/25/2019 STA 2023 Unit 3 Shell Notes (Chapter 6 - 7)

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6-1

Unit 3

Inferential Statistics

Chapter 6: Confidence Intervals

Chapter 7: Hypothesis Testing


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6-2

Chapter 6

Confidence Intervals

6.1: Estimating ( known)

6.2: Estimating ( unknown)6.3: Estimating p


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STA 2023: Elementary Statistics

Section 6.1: Estimating a Population Mean ( known)

Chapters 6 and 7 start inferential statistics: drawing conclusions about population using sample data.

There are two major types of inferential statistics. Use sample data to:

1. Estimate the value of a population parameter (Confidence Intervals)

2. Test some claim about a population parameter (Hypothesis Testing).

Parameter and Statistic Notation

Parameter Statistic

Quantitative Data

(Means)

Population Mean:x

N

= Sample Mean:

xx

n

=

Qualitative Data

(Proportions)Population Proportion:

xp

N= Sample Proportion:

xp

n=

Idea: 1. Estimate the mean weight of an adult male ().

2. Estimate the proportion of adults who currently approve of the president (p).

Point Estimates

A point estimatefor a parameter is asingle valueestimate.

1. For , the best point estimate is :x x

2. Forp, the best point estimate is :p p p

Example 1: Find the point estimate.

a. A sample of 100 adult men has a mean weight of 170 lbs.x= Find the point estimate for , the mean weight of all adult males.

b. A sample of 500 adults showed 240 approved of the president.Find the point estimate forp, the proportion of all adults who approve of the president.


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Interval Estimates (Confidence Intervals)

1. An interval estimateis arange of valuesthat is likelyto contain the parameter.

2. Format: x E= or p p E=

3. A confidence intervalis an interval estimate that comes with a level of confidence, c,

where c is theprobabilitythe interval actually contains the parameter.

Common Confidence Levels:

Interpreting confidence levels:

Theres a 95% chance the interval actually contains

Example 2: Write the confidence interval.

a. A sample of 100 adult men has a mean weight of 170 lbs.x= A 95% confidence interval forthe mean has a margin of error of 3 lbs.

b. A sample of 500 adults gave a 48% approval rating for the president. (90% CI, MOE 3%).

.

Confidence Intervals for Population Mean ( known)

Estimating a population mean, x E= :

1. Get a random sample of size n and compute .x

2. If population is normal or 30 and is known:n

, distributionx N zn

3. To compute theE, first need to findcritical values:

Critical Values,zc

1. Confidence levels, c, are associated with specialz-scores, called critical values, zc2. To find zc, let the confidence level crepresent the middle area of the standard normal curve.

Then find the z-scores than mark the boundaries.

Confidence Level, c 90% 95% 99%

c 0.90 0.95 0.99

1 -c 0.10 0.05 0.01


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Example 3. Find the critical values associated with the following confidence levels.

a. 95%

b. 90%

c. 99%

Confidence Interval for ( known)

Given: is known, the sample is random, and either the population is normal or 30 :n

1. Find the sample statistics andn x

2. Compute the ( 100%c ) confidence interval for a population mean, using:

, wherec

x E E z

n

= =

Interval Notation: x E= or x E x E < < or ( ),x E x E +

Rounding: Round confidence intervals the same as the statistics: one more decimal than data.


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Example 4: A study by researchers at the University of Maryland found the body temperatures of 106

healthy adults had a mean temperature of 98.20F. Assume the population standard deviation is

known to be 0.62F.

a. Construct a 90%, 95%, and 99% confidence interval for the mean body temperature of allhealthy adults.

b. Explain what 95% confidence means in this example.

c. As confidence increases, what happens to the margin of error?


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Example 5:

The Center for Education Reform conducted a study to find the mean salary of public schoolteachers. A random sample of 300 teachers had a mean salary of $41,820. From past studies, thepopulation standard deviation is known to be $2700.

a. Find the 95% confidence interval for the mean salary of all public elementary teachers.

b. If 2000 teachers had been sampled with the same results, what happens to the margin oferror?


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Determining the Sample Size Required to Estimate

To determine what sample size is needed to estimate , first choose:1. Level of confidence2. desired Margin of Error

Then, minimum sample sizerequired to estimate a population mean is

2

cz

n

E

=

,

where nis alwaysrounded up* to the nearest whole number.

If is unknown (common), there are two common ways to estimate it:

1. Get a preliminary sample with 30n and then use s to approximate , or,

2. If you can estimate the range, then approximate usingrange

4

Example 6.

a. A realtor agency wants to estimate the mean number of days a home is on the market before itsells. How many homes must be sampled if they want to be 95% confident the sample mean is

within 10 days of the true population mean? Assume a preliminary study suggests 30 days. =

b. Repeat the above example with different margin of errors (5 days, 3 days, 2 days, 1 day, etc.)What level of confidence and margin of error do you think leads to an acceptable sample size?


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Example 7. Suppose you want estimate the mean weight of an adult male, to be in error by nomore than 3 pounds, and with 95% confidence.

a. Use your knowledge of mens weights to estimate the range and then estimate .

b. How many men would you have to weigh if you want to estimate the mean weight within 3pounds, and with 95% confidence?

c. The CDC conducts annual health surveys to guide research and policies to for preventingpremature mortality (BRFSS System). If they wanted to estimate the mean weight of anadult male within 3 pounds with 99% confidence, what sample size would they need?


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Section 6.2: Estimating a Population Mean (unknown)

Choosing Probability Distributions for Confidence Intervals

known: If is known and either the population is normal or n 30, then , :x Nn

use thestandard normal distributionandcritical z-scores,zcfindE.

unknown: If is unknown and either the population is normal or n 30,

the 'x s will have at-distributionand usecritical t-scores,tc, to findE.

Students t-distribution (withn 1 degrees of freedom)

The t-distribution is a family of curves, each determined by a parameter called the degrees of freedom.

The degrees of freedom are equal to 1 less than the sample size: d.f. = n-1:

Sample Size, n n= 25 n= 15 n= 9

Degrees of Freedom, n 1 d.f = 24 d.f. = 14 d.f = 8

Properties of thetdistribution:1. The t-distribution is bell-shaped and symmetric about its mean.2. The mean = 0, but varies more than the normal distribution.3. As the degrees of freedom increase, the t-distribution approaches the normal distribution.

For n > 30, the t-distribution thez-distribution.

C100% Confidence Interval for ( unknown)

Given: is unknown, the sample is random, and either the population is normal or 30 :n

1. Find the sample statistics , andn x s

2. Compute the ( 100%c ) confidence interval for a population mean, using

, where ,c

sx E E t

n= = and thas 1n degrees of freedom


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Critical Values,tc, for Confidence Intervals

Example 1: Use the t-distribution table to find the critical values. Make a sketch for each.

a. 90% confidence interval, 10n=

b. 95% confidence interval, 18n =

c. 99% confidence interval, 25n =

d. Compare to .c ct z


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Estimating : Choosing the correct distribution

When finding confidence intervals, it is very important to use the correct distribution.

Besides using whether is known or unknown, the distribution of the population and nis also needed:

**Note:

If the population is notnormally distributed and 30,n< neitherthez or t distributions can be used!!

Example 4: State which distribution (z or t)would be used to create a 95% confidence interval forthe population mean, , in the following examples. If neither distribution could be used, explain why.

a. The gestation period of humans is normally distributed with 16= days. A sample of size

12n= has a mean of 267 days.

b. For estimating the mean amount of rainfall during the month of April in Chicago, a simplerandom sample of 36 years has a mean of 3.63 inches and a standard deviation of 1.63 inches.

c. The starting salaries of law school graduates are skewed right with a population standarddeviation of $24,000. A random sample of 15 law school graduates has a mean starting salaryof $63,000.


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Section 6.3 Estimating a Population Proportion,p

Qualitative data and Proportions

Population proportion:

X

p N= ; the proportion (or %) of thepopulationthat has the attribute.

Sample proportion: x

pn

= ; the proportion (or %) of asamplethat has the attribute.

Other notation: 1 ;q p= the proportion (%) of the population thatdoes not have the attribute.

1 ;q p= the proportion (%) of thesamplethat does not have the attribute.

Estimating a population proportion,p

1. Point estimate: p p

2. Confidence Interval estimate: p p E=

3. Notation: p p E= or p E p p E < < + or ( ) ,p E p E +

c100% Confidence Interval for Population Proportion,p

; where

c

pqp p E E z

n= =

1. Use thez-distribution provided: 5 and 5np nq

2. Round proportions and confidence intervals to 3 significant digits.


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Example 1:

In a study conducted by the Centers for Disease Control in 2007, 490 out of 1,700 randomlyselected Americans with a high school diploma were found to be obese.

a. Find a 95% confidence interval for the proportion of high school graduates who are obese.

b. When the same study was performed on Americans with 4 or more years of college education,if was reported that 20.2% of college graduates are obese (based on 95% confidence, and a

margin of error of 2% ). Based on these results, does the obesity rate for high school

graduates appear to be higher than that of college graduates?

Example 2:

An internet company claims that 95% of the products ordered will be mailed within 48 hours of anorder being placed. A random sample of 200 orders showed 174 of the orders were mailed on time.

a. Using a 99% level of confidence, construct a confidence interval for the percentage of allorders that were shipped within 48 hours.

b. Based on your result, does it appear the companys claim is correct? Explain.

c. Do you think this is a good confidence interval? Why or why not?


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Sample Size for Estimating Population Proportionp:

To determine what sample size is needed to estimatep,first choose:

1. Level of confidence2. desired Margin of Error

Then, minimum sample sizerequired to estimate a population proportion is:

1. When an estimate of p is known: or 2. When no estimate of p is known:

2

2

c

z pqn

E=

( )22

0.25c

zn

E=

Again, nis alwaysrounded up tothe nearest whole number.

Example 3: For the internet company in the previous example,

a. What sample size should have been used if they wanted a 3% MOE?

b. What sample size would be needed if they wanted to be 95% confident with a 3% MOE?

Example 4: The National Institute of Drug Abuse wants to estimate the percentage of U.S. teenagersaged 12-18 who have used any illicit drug other than marijuana in the past year. How manyteenagers must be surveyed if they want to be 95% confident that the sample has a margin of error

of no more than 2% ?

a. Assume that there is no available information that could be used as an estimate of p .

b. Assume they use a 2014 estimate that 11% of teenagers had used an illicit drug in the pastyear.


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Chapter 7Hypothesis Testing

7.1: Basic of Hypothesis Testing

7.2: Tests for ( known)

7.3: Tests for ( unknown)7.4: Tests for p


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Section 7.1/7.2: Fundamentals of Hypothesis Testing

Recall:Inferential Statistics draw conclusions about a population based on sample data:

Confidence Intervals:Estimate the valueof a population parameter (using sample statistics).Hypothesis Tests: Tests a claim (hypothesis)about a population parameter (using sample statistics).

Hypothesis test: Tests a claim (hypothesis) about a population parameter, using sample statistics.The claim can be a historical value, a business claim, a product specification, etc.

Components of a hypothesis test: A. The Null and Alternative HypothesesB. The Test Statistic and making decisionsC. Types of Errors in hypothesis testingD. Writing Conclusions about the claim

A. The Hypotheses

Null hypothesis,H0 : - statement about the parameter (,p, )

- assumed true until proven otherwise- must contain equality sign: , , or =

Alternative Hypothesis,Ha: - statement about the parameter that must be true ifHois false.

- must contain: , , or> <

Symbolic Form of the Hypotheses:0

0

:

:

o

a

H

H

=

or

0

0

:

:

o

a

H

H

< or

0

0

:

:

o

a

H

H

>

Note: The original claim* can be in the null or the alternative.

Example 1: Write the claim, the null and alternative hypotheses symbolically.Identify which hypothesis is the original claim.

Make sure you use the correct symbol for the parameter ( ), ,orp

a. Claim: A science group claims normal body temperatures is less than 98.6F.

b. A safety agency claims that at least 70% of cell phone users text while driving.

c. A quality control engineer says the diameters of bike tires have a standard deviation of 0.05inches.


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B. Making Decisions

1. State hypotheses. **Assume 0H is true.

2. Collect sample data (test statistic).

3. Make a decision about 0H : a. RejectH0 ( accept aH ) ,or,

b. Fail to RejectH0( cant acceptHa).

Example 2. Consider the scenario of a trial, where the defendant is presumed innocent until provenotherwise. Set up a hypothesis test and explain the two decisions that can be made.

C. Types of Errors

1. Type I error: 0 0Reject H H is actually true

2. Type II error: 0 0FTR H H is actually false

The symbol is used to represent the probability of a Type I error: ( )Type I errorP =

The symbol is used to represent the probability of a Type II error: ( )Type II errorP = Note: is set in advance of starting the test, and is also known as the level of significance of the test.

Example 3: Identify the Type I and Type II errors associated with the following claims orhypotheses, and the possible consequences of those errors.

a. From the trial in the previous example, the claim of innocent until proven guilty.

b. A bottling company claims the mean amount of coke in a coke can is 12 oz. This isperiodically checked by quality control personnel.


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D. Writing conclusions (in terms of the original claim)

After making a decision about the null, a final conclusion is written about the original claim. How theconclusion is worded depends on the decision, and whether the claim was in Ho or Ha.

Ho contains claim:

1. Reject Ho: There is enough evidence torejectclaim that Ho

2. FTR Ho: There isnotenough evidence torejectthe claim that Ho

Ha contains claim:

1. Reject Ho: There is enough evidence tosupportthe claim that Ha

2. FTR Ho: There isnotenough evidence tosupportthe claim that Ha

Example 4: Write the conclusion for the hypothesis test based on the given decision.

a. Researchers at the University of Maryland claims that the mean body temperature of healthy

adults is less than 98.6F. The decision was Reject 0H .

b. A safety agency claims that at least 70% of cell phone users text while driving.

The decision was FTR 0H .


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Critical Region

E. How to make a decision about the Null Hypothesis

1. Write claim. State ,o aH H . Assume 0H is true. ( 0 = ). Determine the tails of the test.

2. Get test statistic: value from sample data; used to make a decision about 0H .

For tests about , usex . Convert x to a standard score ( )orz t

3. Make a decision whether to reject the 0H , using: a. Critical Region Method, orb. P-value method

We start with tests for a population mean, .

For known and either x N or 30 :n ( )0 ,x N n

Tails of the Test and the Critical Region Method

Tails of the test: Assuming the null hypothesis 0H is true, where would your sample mean

x have to fall to convince you to reject 0H (and accept aH )?

Critical Region: Region under the curve where values of test statistic that would be unlikely,

assuming 0H is true.

Area of critical region = ( is thesignificance levelof the test)

Critical Values: Values (zcortc)that bound the critical region

Decision: If test statistic x falls in the critical region, reject Ho.

If test statistic x falls in the non-critical region, FTR Ho.

1. Left Tailed Test 0 0

0

:

:a

H

H

3. Two Tailed Test 0 0

0

:

:a

H

H

=


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The P-value Method of Making Decisions

Instead of determining whether your sample mean is unusual by whether or not it falls in acritical region, be more precise andfind the p-value:

P-value: Probabilityof getting a test statistic as extreme or more than the one from the sample data,assumingHois true.

1. Select level of significance, . (How unusual would your sample have to be to reject Ho?)

2. Gather a sample. Compute x and covert to a standard test statistic, *.z 2. Determine the tails of the test.3. Compute the P-value.

4. Make a decision: a. If P-value (unusual), Reject Ho.b. If P-value > (not unusual), FTR Ho.

1. Left Tailed Test

0 0

0

:

:a

H

H

3. Two Tailed Test

0 0

0

:

:a

H

H

=


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Example 5: Make a decision about the Ho, under the given conditions with the indicated method.

Critical Region Method

Sketch, shade the critical region (area = ),find the critical values, make a decision

P-value Method

Sketch, shade the P-value area,find the P-value, make a decision

left-tailed test, 0.05, 1.73z= = left-tailed test, 0.05, 1.73z= =

right-tailed test, 0.01, 2.07z= = right-tailed test, 0.01, 2.07z= =

two-tailed test, 0.05, 1.81z= = two-tailed test, 0.05, 1.81z= =


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STA 2023: Section 7.2

Hypothesis Test about Population Mean ( known)

Method: Given is known, the sample is random, and either the population is normal or 30,n

use thez-testfor the population mean :

1. Write the claim in terms of .

Use the claim to write ,o aH H . Assume 0H is true. (i.e., 0 = )

Determine whether it is a left tailed test, right-tailed test, or 2-tailed test.

Note the level of significance, .

2. Get sample test statistic, .x For known and either x N or 30 :n ( )0 ,x N n

Convert x to a standard test statistic:x

zn

=

3. Sketch the sampling distribution forx .Indicate on the sketch whether it is a left tailed test, right-tailed test, or 2-tailed test.

Make a decision about 0H based on the test statistic and given significance level , using:

a. Critical Region method: Shade the critical region, find the critical values,c

z

If z is in the critical region, reject 0H

If z is not in the critical region, fail to reject 0H

b. P-value method: Find the probability of the test statistic being as extreme or more as thesample:

If 0, reject HP < If 0, fail to rejectP H

4. Interpret your decision by writing a conclusion in terms of the original claim.


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For each of the following: State the claim, write the hypotheses, find the test statistic, sketch the samplingdistribution, use both the critical region method and the p-value method to make a decision about Ho, andinterpret your decision in terms of the original claim.

Example 1:Fire insurance rates for a certain suburb are based on past data that states mean distance from a homein the community to the nearest fire department is 4.7 miles. Residents in the community claim the

mean distance is less, and want their rates lowered. From a random sample of 64 homes in thesuburb, the mean distance was 4.3 miles. Assume the population standard deviation was 2.4 miles.Use the data to test the claim that the mean distance to the nearest fire station is less than 4.7 miles.Use a 1% level of significance.


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Example 2:

Golf course designers are concerned that old courses are becoming obsolete because new equipmentenables golfers to hit the ball so far: In effect, golf courses are shrinking. One designer claims thatnew courses need to be built with the expectation that players will be able to hit the ball more than 250yards (with their drivers), on average. Suppose a sample of 135 golfers is tested, and their mean

driving distance is 256.3 yards. Assume the population standard deviation is 43.4 yards. At 0.05= ,can you support the designers claim?


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Example 3:

Many colleges across a certain state have long used the CPT placement test for placing students intothe appropriate math courses. Historically, the mean score on the CPT has been 82. The school isconsidering switching to a new placement test called COMPASS. The COMPASS test is easier toadminister and less expensive, but the college is unwilling to switch if the COMPASS test results in adifferent mean than the CPT. An independent testing agency tested 36 students, which gave a meanof 79. Past studies show the population is normally distributed with a standard deviation of 8. Use

this information to test the COMPASS claim that their test has the same mean as the CPT. Use0.05.=

b. In the context of this problem, what is a Type I error? Is 0.05= appropriate?


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Section 7.3: Hypothesis Test for Population Mean ( unknown)

Method: Given is unknown, the sample is random, andeither the population is normal or 30,n

use thet-testfor the population mean :

1. Write the claim in terms of .

Use the claim to write ,o aH H . Assume 0H is true. (i.e., 0 = )

Determine whether it is a left tailed test, right-tailed test, or 2-tailed test.

Note the level of significance, .

2. Get the sample test statistic, , and .x s

For unknown and either x N or 30,n use the t-distribution with 1n degrees of freedom.

Convert x to a standard test statistic: xts n

=

3. Sketch the sampling distribution forx .Indicate on the sketch whether it is a left tailed test, right-tailed test, or 2-tailed test.

Make a decision about 0H based on the test statistic and given significance level , using:

a. Critical Region method: Shade the critical region, find the critical values,c

z

If z is in the critical region, reject 0H

If z is not in the critical region, fail to reject 0H

b. P-value method: Find the probability of the test statistic being as extreme or more as thesample:

If 0, reject HP <

If 0, fail to rejectP H

4. Interpret your decision by writing a conclusion in terms of the original claim.


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Example 1: Use the t-distribution to make a decision about the Ho under the given conditions.

Critical Region Method

Sketch, shade the critical region (area = ),find the critical values, make a decision

P-value Method (software)

Sketch, shade the P-value area,find the P-value, make a decision

a. right tailed test, 0.01, 25, 2.516n t= = = right tailed test, 0.01, 25, 2.516n t= = =

b. left tailed test, 0.05, 10, 1.63n t= = = left tailed test, 0.05, 10, 1.63n t= = =

c. 2 tailed test, 0.05, 35, 2.103n t= = = 2 tailed test, 0.05, 35, 2.103n t= = =


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For each of the following: State the claim, write the hypotheses, find the test statistic, sketch the samplingdistribution, use either the critical region method or the p-value method to make a decision about Ho, andwrite your conclusion in terms of the original claim.

Example 2:A group of researchers conducted a study of the birth weights of babies born to women who smokedregularly while they were pregnant. For a sample of 32 such women, the mean birth weight of the

babies was 3,160 grams and the standard deviation of 440 grams. Test the hypothesis that the meanbirth weight of babies born to mothers who smoke is less than 3370 g (the mean birth weight for all

babies). Use = 0.01.


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Example 3.

a. A car company claims that the mean gas mileage for its luxury sedan is more than 28 mpg inthe city. To test the claim, the company randomly selects 10 sedans, giving the mpg shown below.

Use a level of significance of = 0.01. Assume the mpg for all such sedans has an approximatelynormal distribution.

29.1 30.6 27.8 32.4 28.0 27.9 29.2 30.1 28.0 28.4

b. Notice the claim was more than 28 mpg. Why not say at least 28 mpg?


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Section 7.4: Testing a claim about a Population Proportion

Recall: Qualitative data and Proportions

Population proportion:

X

p N= ; the proportion of thepopulationthat has the attribute.

1 ;q p= the proportion of the population thatdoes not have the attribute.

Sample proportion: x

pn

= ; the proportion of asamplethat has the attribute.

1 ;q p= the proportion of thesamplethat does not have the attribute. .

Hypothesis Tests for Population Proportion

( )

0

0

:

:

Two tailed

o

a

H p p

H p p= or

( )

0

0

:

:

Left tailed

o

a

H p p

H p p< or

( )

0

0

:

:

Right tailed

o

a

H p p

H p p>

Hypothesis Test for Population Proportion

1. Write the claim in terms ofp.

Use the claim to write ,o aH H . Assume 0H is true. (i.e. 0p p= )

Determine whether you are doing a left tailed, right tailed, or 2-tailed test.

2. Get sample test statistic, .p For large samples, 5 and 5np nq : , pqp N pn

.

Convert p to a standard test statistic,z:p p

zpq

n

= **

3. Sketch the sampling distribution forp .

Indicate on the sketch whether youre doing a left-tailed test, a right-tailed test, or a 2-tailed test.

Based on the test statistics, make a decision about 0H using:

a. Critical Region Method (shade critical region, find critical values,zc).b. P-value method: shade and find the P-value area.

4. Interpret your decision in terms of the original claim.

Note**: When the calculation of p results in a decimal with many places, store the number on your

calculator and use all the decimals when evaluating theztest statistic.

Large errors inz and the P-value can result from rounding p too much.


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For each of the following: State the claim, write the hypotheses, find the test statistic, sketch the samplingdistribution, use the critical region or P-value method to make a decision about Ho, and interpret yourdecision in terms of the original claim.

Example 1:In a survey conducted by the Gallop Organization in 2011, 456 of 1012 adults aged 18 years or oldersaid they had a gun in the house. In 2010, 41% of households had a gun. Is there sufficient evidence

to support the claim that the proportion of households that have a gun has changed from 2010 to2011? Use a 5% level of significance.


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Example 2:

Pepcid is a drug that can be used to heal duodenal ulcers. Suppose the manufacturer of Pepcid claimsthat more than 80% of patients are healed after taking 40 mg of Pepcid every night for 8 weeks. Inclinical trials, 148 of 178 patients suffering from duodenal ulcers were healed after 8 weeks. Test the

manufacturers claim at 0.01= level of significance.


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Exam 3 Review: Chapters 6 & 7 (Larson, 6thed)

Below is a list of topics for the exam. Review class notes, homework, and quizzes.Complete the review problems in MML.Additional review can be found in the electronic textbook (see next page).

Chapter 6: Confidence Intervals

1. Construct and interpret confidence intervals

2. Estimating : x E=

a. or 30 andx N n known: usezdistribution: cE zn

=

b. or 30 andx N n unknown: use tdistribution: cs

E tn

=

3. Estimating p :

;c

pqp p E E z

n

= = (provided and 5np nq )

4. Sample sizes

a. for:2

cz

nE

=

b. forp:( )

( )2

2

0.25 Proportion , unknownc

zn p q

E= ( )

2

2

Proportion , knownc

z pqn p q

E=

Chapter 7: Hypothesis Testing

1. Understand: claim, null and alternative hypothesis, decisions, Type I and Type II errors,

significance level

2. Conduct hypothesis tests for population mean or a population proportionpby:

State the claim, write the hypotheses, find the standard test statistic, sketch the samplingdistribution, use either the critical region method or p-value method to make a decision about Ho,and interpret your decision in terms of the original claim.

a. Critical region method: Shade the critical region (area = ), find the critical valuesb. P-value method: Find probability of getting a test statistic as extreme or more as the

sample; compare to

3. Test statistics and distributions:

a. For tests about : or 30,x N n known: usezdistribution:x

zn

=

b. For tests about : or 30,x N n unknown: use tdistribution:x

ts n

=

c. For tests aboutp: ( 5, 5np nq> > ): usez distribution, p pzpq

n

=


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Review Problems

*1. MyMathLab: Test 3 Review (Chapters 6 and 7)

2. Optional Review: Chapter Quizzes with VideosChapter Quizzes: MML, Electronic Textbook, Chapter #, Chapter Quiz and VideosStudent Solutions Manual: MML, Student Solutions Manual, Chapter #

Chapter 6 Quiz: All 1-5;Chapter 7 Quiz: All 1-5

sta 2023 unit 3 shell notes (chapter 6 - 7)

Documents