Graded Worksheet D1Name: ________________ This needs to be completed and emailed to burelle@hartford.edu by the due date announced in Course Compass. For the situation described, complete the following.Use StatCrunch to do the calculations, explaining briefly what you entered into StatCrunch, and being sure to identify your answers clearly. 1.At a large university, the dean of students wonders if the percentage of first generation students has changed since he arrived 10 years earlier.When he arrived, the proportion was 53%.He randomly samples 93 students, finding that 58 are first-generation. a.State the null and alternative hypotheses using proper notation. b.Use StatCrunch to calculate the test statistic (z) and P-value. c.At = 0.05, do you reject the null hypothesis?YES / NO d.Write a sentence summarizing your finding in the context of the problem. 2.Using the data from problem 1, calculate a 95% confidence interval.a.Use StatCrunch to calculate the confidence interval.Write your answer in a form similar to (15.44%, 18.36%).

b.Write a sentence summarizing your findings in the context of the problem. page 2 A manufacturer uses two machines to drill holes in pieces of sheet metal used in engine construction.The production manager is interested in knowing whether one machine produces more defective drillings than the other. Here is the data from one day of production, which we will treat as a random sample from all the parts produced by the machines. Number defective Number not defective Total Machine 131191222 Machine 238143181 Whole sample69334403 1.Use the data to fill in the following contingency table which takes which machine as the explanatory variable.The sum of each row should be 100%, except for possible rounding. DefectiveNot defectiveTotals Machine 1 13.9786.03 100% Machine 2 2179 100% Whole sample 17.1282.88 100% 2.Based on these percentage calculations, we can see that in the sample, there is a difference between the two machines.To determine whether this is a significant difference (that is, one that suggests a difference in the entire population), you will carry out a 2-test using the following steps. a.Write the null hypothesis using the word correlation or the word association. b.Write the null hypothesis using words such as dependent, independent, depends on. c.Fill in the table of expected counts. Expected countsDefectiveNot defectiveTotals Machine 1 38.0099183.99007 222 Machine 2 30.99007150.0099256 181 Whole sample69334403 page 3 d.Fill in the table showing the2 calculation for each cell. 2 calculation DefectiveNot defective Machine 1 1.29.27 Machine 2 1.59.33 e.Find the total 2 value, and use the StatCrunch chi-square calculator to calculate the P-value. Total x2 value = 3.4731 Pvalue= .05 f.At = 0.01, is there a significant difference between the two machines?YES / NO g.Fill in the blanks.At = 0.05, we _____________ (did / did not) find evidence that there (is / is not) an association between which machine it was and whether the part was defective. h.Fill in the blanks.At = 0.05, we _____________ (did / did not) find evidence that whether a part is defective ________(is / is not) dependent on which machine made the part. 1.You are doing a chi-square test with a 5 by 9 table of counts (that is, 5 rows and 9 columns). a.What is the degrees of freedom? 4 or 8 b.Suppose you get 2 = 45.23.Calculate the p-value. P=.00001 2.Use StatCrunch to calculate the test statistic (that is, the 2 value) and the P-value for this contingency table, which shows the income level for a random sample of adults cross classified by gender.(In order to answer question #3, have StatCrunch give you the expected counts when it runs the hypothesis test.) LowMiddleHighTotal Male23302982 Female26282074 Total495649156 X2 value = 1.4994 page 4 P value= .4725 3.By examining the StatCrunch output, give the table of expected counts for the data in problem #2.LowMiddleHighTotal Male 25.7630.15 25.7682 Female 23.2426.56 23.2474 Total495649156 4.( YES/NO ) Based on the data in problem #2, there is a significant association between gender and income level (use significance level 0.05). 5.( YES/NO ) Based on the data in problem #2, there is a significant difference between the income levels for the two groups (males, females) (use significance level 0.01). In a large survey of U.S. college students, 1630 of the 7180 men self-identified as binge drinkers, and 1684 of the 9916 women self-identified as binge drinkers. 1.Calculate the proportion for the men (

) and the proportion for the women (

). Pmen=.227 pwomen= .169826543 2.Calculate a point estimate for the ratio of the proportions for the two populations, using

/

.Fill in the blank: In the sample, men were _________1.3368___ times as likely to be binge drinkers as women (that is, ______5.72______ % more likely). 3.Calculate a point estimate for the difference between the proportions, using

. .0572 4.Use StatCrunch to calculate a 95% confidence interval for the difference between the two proportions.Tell what you put into StatCrunch, and write the confidence interval in a form similar to (55.17%, 83.21%). page 5 5.Based on the interval, is it feasible that the proportions are actually the same for the two populations? (YES / NO)