math 14

Quiz 3 MA 1510 Student: ___________________________________________________________________________ Each question is worth 5 points for a total of 100 points for the quiz.

Show work where applicable. Partial credit is possible. You can submit an Excel spreadsheet if you use

Excel for any of the calculations but be sure you clearly identify the question number with the calculation.

This quiz is given under the honor system. You may use your text and notes, but you may not confer with

anyone to answer the questions.

The quiz must be submitted by 9pm, Sunday May 4, 2014.

1. Which of the following is a point estimate for the population mean (µ)? A. σ B. s C. x/n D. ̅ 2. A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted.

The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

A. 6.99 and 7.99 B. 4.15 and 7.15 C. 6.14 and 6.86 D. 6.49 and 7.49

3. Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?

A. 69.2% to 86.4% B. 78.2% to 81.8% C. 76.5% to 83.5% D. 77.7% to 82.3%

4. A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave?

A. $323.40 to $426.60 B. $328.40 to $421.60 C. $350.80 to $395.80 D. $369.32 to $380.68

5. The mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.90 degree of confidence. For a small pilot study, the mean was 150 days and the standard deviation was 14 days. If the population mean is estimated within two days, how many salespeople should be sampled?

A. 133 B. 452 C. 511 D. 2,100

6. A confidence interval for a population mean __________. A. Estimates the population range B. Estimates a likely interval for a population mean C. Estimates likelihood or probability D. Estimates the population standard deviation

7. A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. The null hypothesis is ______.

A. H0: µ = 6.6 B. H0: µ ≥ 6.6 C. H0: µ > 7.6 D. H0: µ ≤ 7.6

Questions 8 - 11: The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per

term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05.

8. What are the null and alternative hypotheses for this study? A. H0: µ ≤ $9,000; H1: µ > $9,000 B. H0: µ ≥ $9,000; H1: µ < $9,000 C. H0: µ ≤ $8,500; H1: µ > $8,500 D. H0: µ ≥ $8,500; H1: µ < $8,500

9. What is the test statistic for this test? A. ±3.82 B. +0.204 C. -3.82 D. +3.82

10. What is the p-value for this test? A. 0.0001 B. 0.0124 C. 0.0500 D. 0.4938

11. Let α = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost? A. Equal to $8,500 B. Greater than $8,500 C. Less than $8,500 D. Not equal to $8,500

12. It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the sample proportion?

A. 0.10 B. 0.125 C. 40 D. 0.40

13. For an alternate hypothesis: µ > 6,700, where is the rejection region for the hypothesis test located? A. In both tails B. In the left or lower tail C. In the right or upper tail D. In the center

14. In a market test of a new chocolate raspberry coffee, a poll of 400 people from Dobbs Ferry showed 250 preferred the new coffee. In Irvington, 170 out of 350 people preferred the new coffee. To test the hypothesis that there is no difference in preferences between the two villages, what is the null hypothesis?

A. H0: π1 < π2 B. H0: π1 > π2 C. H0: π1 ≠ π2 D. H0: π1 = π2

15. A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next.

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the alternate hypothesis?

A. H1: µA = µB B. H1: µA ≠ µB C. H1: µA ≤ µB D. H1: µA > µB

16. An investigation of the effectiveness of a training program to improve customer relationships included a pre- training and post-training customer survey. To compare the differences, they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow.

This analysis is an example of _____________. A. A one-sample test of means B. A two-sample test of means C. A paired t-test D. A test of proportions

17. If the correlation between two variables is close to one, the association between the variables is ___________. A. Strong B. Moderate C. Weak D. Zero

18. In the regression equation, what does the letter "X" represent?

A. The dependent variable B. The independent variable C. The slope of the line D. The Y-intercept

19. Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal? A. 5,734 B. 8,000 C. 4,601 D. 4,050

20. If the of determination is 0.94, what can we say about the relationship between two variables?

A. The strength of the relationship is 0.94. B. 94% of the total variation of the dependent variable is explained by the independent variable. C. The direction of the relationship is negative. D. The direction of the relationship is positive.