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quiz_3_stats.pdf
Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Name: __________________________ Pace email: [email protected]
Check the box for your class: Traditional Online
For all manual computations on a calculator use all of the digits available. Do not round or truncate intermediate results. Report your answers using all available digits on your calculator or computer unless told otherwise. Trailing 0s need not be
written down. If you need to use special symbols like µ (mu), σ (sigma), and (x-bar) you may spell out the symbol rather than type it into your answers if you do not know how to enter the symbols into your answer sheet. When handing in your quiz be sure to change the name of this file to your LastnameFirstNameQ3.pdf. All questions worth 4 points each.
1. True or False: A scatter-plot can help determine if two variables are related in some systematic way. 1. _______________
2. True or False: The correlation coefficient can only range between 0 and 1. 2. _______________
3. True or False: The value −0.75 of a population correlation coefficient indicates a stronger linear relationship than that of 0.60. 3. _______________
4. True or False: A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations. 4. _______________
5. True or False: For any sample size n, the sampling distribution of is normal if the population from which the sample is drawn is uniformly distributed. 5. _______________
X
X
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Questions 6–9: A Massachusetts state police officer measured the speed of 100 motorists on the Massachusetts Turnpike and found that 70 exceeded the posted speed limit by more than 10 miles per hour. The police officer claims that more than 60% of motorists drive at least 10 miles per hour more than the posted speed on the turnpike.
6. Specify the null and alternative hypotheses to test the officer’s claim.
6. Ho: _________________________________ vs. Ha: _________________________________
7. Calculate the value of the test statistic. 7. _______________
8. What is the p-value of the test statistic? 8. _______________
9. At the 5% significance level, does the evidence support the officer’s claim? Explain in terms of p-values.
9. ______________________________________________________________________________________
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Questions 10–13: The student senate at a local university is about to hold elections. A representative from the women’s sports program and a representative from the men’s sports program must both be elected. Two candidates, an incumbent and a challenger, are vying for each position and early polling results are presented next. A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates. In a sample of 100 voters, 67 said that they would vote for the women’s incumbent candidate. In a separate sample of 100 voters, 55 said they would vote for the men’s incumbent candidate. Let pw and pm be the
proportions of supporting votes for the incumbent candidates representing women’s and men’s sports programs, respectively.
10. Specify the null and alternative hypotheses, in terms of pw and pm, to determine
whether the percentages of supporting votes are different between the two incumbent candidates?
10. Ho: _________________________________ vs. Ha: _________________________________
11. What is the value of the test statistic used to test the hypotheses? 11. _______________
12. What is the critical value(s) of the test statistic to test the hypotheses at the 5% level of significance? 12. _______________
13. At the 5% significance level, can you determine if the difference in the percentages are statistically? Explain on terms of the critical value and test statistic above.
13. _____________________________________________________________________________________
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Questions 14 & 15:Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars): $1,743 $1,438, $1,212, $1,705, $1,985, $1,857, & $1,916. Assume that profits are normally distributed.
14. Give appropriate hypotheses to test Becky’s concern?
14. Ho: _________________________________ vs. Ha: _________________________________
15. What is the value of the appropriate test statistic? 15. _______________
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Questions 16 & 17: A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertis- ing (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He believes the model: is appropriate where the standard regression model holds. The following
ANOVA table shows a portion of the regression results.
16. Use the sample regression line to predict Sales for a firm with Advertising of $500? Be sure to specify units in your answer. 16. _______________
17. Do you believe that there is a linear relationship between Advertising and Sales. Explain your reasoning using a 5% level of significance.
17. ______________________________________________________________________________________
Sales 0 1Adversting + +=
Regression Analysis
r2 0.135 n 25 r 0.367 k 1
Std. Error of Estimate 4.681 Dep. Var. Sales
Regression output confidence interval variables coefficients std. error t (df=23) p-value 95% lower 95% upper Intercept a = 40.100 14.080 2.848 0.0052 10.973 69.227
Adversting b = 2.880 1.520 -1.895 0.0608 -0.264 6.024
ANOVA table Source SS df MS F p-value
Regression 78.530 1 78.530 3.58 0.0608 Residual 504.020 23 21.914
Total 582.550 24
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Questions 18–20: A university has six colleges and takes a poll to gauge student support for a tuition increase. The university wants to ensure each college is represented fairly. The below table shows the observed number of stu- dents who participate in the poll from each college and the actual proportion of students in each college.
18. What Ho and Ha should be tested?
18. Ho: ______________________________________________________________________
vs.
Ha: _____________________________________________________________________
19. What is the value of the test statistic? 19. _______________
20. What is the p-value of the test statistic? 20. _______________
College Observed Proportion 1 457 0.20 2 206 0.10 3 301 0.10 4 792 0.30 5 336 0.15 6 373 0.15
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
Questions 21–23: In the following table, individuals are cross-classified by their age group and income level.
We want to test if the Income level and Age Group are independent.
21. What is the value of the test statistic? 21. _______________
22. What is the critical value(s) of the test statistic if α=5%. 22. _______________
23. Should we reject the null hypothesis? Explain in terms of the critical value given above.
23. ______________________________________________________________________________________
24. True or False: We always deal with matched-pairs sampling if two samples have the same number of observations when testing for equality of population means. 24. _______________
Income Age Low Medium High 21–35 120 100 75 36–50 150 160 100 51–65 160 180 160
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Pace University MAT 117 CRN 21371 & 20372 Prof. Kazlow
Mat 117 Spring 2017 Quiz 3 May 1–3
25. A farmer uses a lot of fertilizer to grow his crops. The farmer’s manager thinks fertilizer products from distrib- utor A contain more of the nitrogen that his plants need than distributor B’s fertilizer does. He takes two inde- pendent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µA and µB represent the average amount of nitrogen per batch for fertilizer’s A and B, respec-
tively. Which of the following is the appropriate conclusion at the 5% significance level?
25. _______________
A. Reject Ho; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
B. Reject Ho; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
C. Fail to reject Ho; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
D. Fail to reject Ho; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
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