Test 11A

PreTest 11A

AP Statistics

Name:KEY

Directions: Work on these sheets. Tables and formulas appear on a separate sheet.Part 1: Multiple Choice. Circle the letter corresponding to the best answer1. DDT is an insecticide that accumulates up the food chain. Predator birds can be contaminated with quite high levels of the chemical by eating many lightly contaminated prey. One effect of DDT upon birds is to inhibit the production of the enzyme carbonic anhydrase, which controls calcium metabolism. It is believed that this causes eggshells to be thinner and weaker than normal and makes the eggs more prone to breakage. (This is one of the reasons why the condor in California is near extinction.) An experiment was conducted where 16 sparrow hawks were fed a mixture of 3 ppm dieldrin and 15 ppm DDT (a combination often found in contaminated prey). The first egg laid by each bird was measured, and the mean shell thickness was found to be 0.19 mm. A normal eggshell has a mean thickness of 0.2 mm.

The null and alternative hypotheses are

(a)

(b)

(c)

(d)

(e)

2.A significance test allows you to reject a hypothesis in favor of an alternative Ha at the 5% level of significance. What can you say about significance at the 1% level?

(a)

can be rejected at the 1% level of significance.

(b)There is insufficient evidence to reject at the 1% level of significance.

(c)There is sufficient evidence to accept at the 1% level of significance.

(d)Ha can be rejected at the 1% level of significance.

(e)The answer cant be determined from the information given.

3.In a test of H0: = 100 against Ha: 100, a sample of size 80 produces z = 0.8 for the value of the test statistic. The P-value of the test is thus equal to

(a) 0.20

(b) 0.40

(c) 0.29

(d) 0.42

(e) 0.21

4.Which of the following is/are correct?

I.The power of a significance test depends on the alternative value of the parameter.

II.The probability of a Type II error is equal to the significance level of the test.

III.Type I and Type II errors make sense only when a significance level has been chosen in advance.

(a)I and II only

(b)I and III only

(c) II and III only

(d)I, II, and III

(e)None of the above gives the complete set of correct responses.

5.A 95% confidence interval for is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H0: = 0 versus Ha: 0 at the ( = 0.05 level, using the same data as used to construct the confidence interval.

(a) We cannot test the hypothesis without the original data.

(b) We cannot test the hypothesis at the ( = 0.05 level since the ( = 0.05 test is connected to the 97.5% confidence interval.

(c) We can make the connection between hypothesis tests and confidence intervals only if the sample sizes are large.

(d) We would reject H0 at level ( = 0.05.

(e) We would accept H0 at level ( = 0.05.

6. Here's a quote from a medical journal: An uncontrolled experiment in 17 women found a significantly improved mean clinical symptom score after treatment. Methodologic flaws make it difficult to interpret the results of this study. The authors of this paper are skeptical about the significant improvement because

(a)there is no control group, so the improvement might be due to the placebo effect or to the fact that many medical conditions improve over time.

(b) the P-value given was P = 0.03, which is too large to be convincing.

(c) the response variable might not have an exactly Normal distribution in the population.

(d) the study didnt use enough subjects to achieve any statistically significant findings.

(e) the mean is not resistant.

7.A medical experiment compared the herb echinacea with a placebo for preventing colds. One response variable was volume of nasal secretions (if you have a cold, you blow your nose a lot). Take the average volume of nasal secretions in people without colds to be = 1. An increase to

= 3 indicates a cold. The significance level of a test of versus is

(a)the probability that the test rejects when = 1 is true.

(b) the probability that the test rejects when = 3 is true.

(c) the probability that the test fails to reject when = 3 is true.

(d) the probability that the test fails to reject when = 1 is true.

(e) none of the above

8.A radio show runs a phone-in survey each morning. One morning the show asked its listeners whether they would prefer Congress or the president to set policy for the nation. The majority of those phoning in their responses answered Congress, and the station reported the results as statistically significant. We may safely conclude that

(a)there is deep discontent in the nation with the president.

(b)it is unlikely that, if all Americans were asked their opinion, the result would differ from that obtained in the poll.

(c)there is strong evidence that the majority of Americans prefer Congress to set national policy.

(d)very few people other than the majority of those phoning in their responses prefer Congress to set policy for the nation.

(e)that the majority of Americans would actually prefer the president to set policy, because of the biased method of data collection.

Part 2: Free Response

Communicate your thinking clearly and completely.

9. Acid rain is a serious problem in Canada. In many cases, lakes become so acidified that they cannot support any significant fish life. One possible (and very costly!) solution is to try to mitigate the effects by dumping crushed limestone into the lakes. This will neutralize the acidity. The following are actual data from a study of such an intervention in a lake.

From enormous samples at other control lakes, it is reasonable to assume that under the acidic conditions the weight of individual fish of a particular age class is Normally distributed with a known mean of 3250 grams (g). One year after the addition of limestone, a sample of 22 fish was taken and the weight of the individual fish was obtained. Here are the sorted data (g):

1595 1605 1634 2633 2864 2924 3035 3051 3293 3344 3381

3398 3421 3446 3514 3614 3694 3739 3756 3788 3898 3952

Before the analysis began, it was noticed that several fish had abnormally low weights (below 2000 g). After further investigation it was noted that these fish had ingested pieces of plastic from litterbugs' foam cups and could not properly digest food. The study's method of analysis was to delete all values less than 2000 g. After deleting such values, = 3407.6 g. Assume that grams for the weights of fish after limestone is added.

(a) Carry out an appropriate significance test at the 5% significance level to determine whether the mean weight of the fish in the lake increased after the limestone was added.

(b) Would your conclusion in (a) have changed if the outliers had been included in the analysis? Justify your answer with appropriate statistical evidence.

We dont know if the weights of all fish are normally distributed and the sample size is not large enough to use the CLT to ensure Normality in the sampling distribution. Outliers in the sample would suggest that it did not come from a Normal Population and would violate the conditions for inference.

10. When the manufacturing process is working properly, NeverReady batteries have lifetimes that

follow a right-skewed distribution with hours and hours. A quality control supervisor selects a simple random sample of n batteries every hour and measures the lifetime of each. If she is convinced that the mean lifetime of all batteries produced that hour is less than 7 hours at the 5% significance level, then all those batteries are discarded.

(a) State appropriate hypotheses for the quality control supervisor to test.

(b) Describe a Type I and a Type II error in this situation, and explain which is more serious.

Type I: When the supervisor decided the mean lifetime of the batteries was less than 7 hours and discarded all the batteries when the process is actually working properly

Type II: If she decided the process is working fine when in fact the batteries lifetime was less than 7 hours.

Type I would mean loss of revenue for the company, but a Type II error would mean sending out substandard material and giving the company a bad name.Since testing the lifetime of a battery requires draining the battery completely, the supervisor wants to sample as few batteries as possible from each hours production. She is considering a sample size of n = 4.

(c) Explain why this sample size may lead to problems in carrying out the significance test from

(a). Reducing sample size will reduce the power of the test.that is the likelihood of finding a problem with the process when there really is one.(d) Would this sample size give the supervisor sufficient power to detect that the actual mean

lifetime for batteries produced that hour was hours? Justify your answer.

Power = .2 (a very low value) This sample does not give the supervisor sufficient power

(e)Would you recommend that the quality control supervisor use a significance level of or in future tests? Explain.

Recommend using = .1 because increasing the significance level is another method of increasing power.

(or = .01 if you can justify wanting to reduce the chance of a Type I error.)

Chapter 113PreTest 11A

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