MAT 312

Test 2 Chapters 8, 9 & 12 (180 Total Points)

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1. Construct a 95% confidence interval for the mean of a normal population if a random sample of size 60 from the population yields a sample mean of 90 and the population has a standard deviation of 10. What is the confidence interval and margin of error (10 points)?

2. Forty panels were exposed to various corrosive conditions to measure the protective ability of paint. The mean life for the samples was 112 hours. The life of the paint samples is assumed to be normally distributed with a population standard deviation of 25 hours. Find the 85% confidence interval and margin of error for the mean life of the paint (10 points).

3. Construct a 98% confidence interval for the mean of a normal population assuming that the values listed below comprise a random sample taken from the population. The population standard deviation is unknown. Also, what are the mean and sample standard deviation (15 points).

4. Suppose you sample 19 baseball pitchers and find that they have an average pitching speed of 87 mph with a standard deviation of 0.98 mph. Find a 95% confidence interval for the average pitching speed of all pitchers (10 points).

5. A tire manufacturer is testing the tire pressure in its new tires. A random sample of 10 tire pressure readings, yield a variance of 31.8. Construct and interpret a 95% confidence interval for the variance (10 points).

6. Find the t – value such that .025 area of the area under the curve is to the left of the t – value. Assume the degree of freedom is 100 (5 points).

7. Find t_α/2,n-1 for area two tails the following combinations of α and n (5 points each):
8. α=.05, n=25
9. α=.20, n=3

8. Find z_α/2 for the following confidence levels (5 points each):
9. 80%
10. 70%
11. Find z_α/2 for the following levels of α (5 points each):
12. α=.66
13. α=.30

10. A state politician is interested in knowing how voters in rural areas and cities differ in their opinions about gun control. For his study, 80 rural voters were surveyed, and 47 were found to support gun control. Also, 80 voters from the cities were surveyed, and 59 of these voters were found to support gun control. Construct and interpret a 90% confidence interval and margin of error for the true difference between the proportion of rural and city voters who favor gun control (10 points).

11. John believes that his wife’s cell phone battery does not last as long as his cell phone battery. On eight different occasions, he measured the length of time his cell phone battery lasted, and calculated that the mean was 26.9 hours with a standard deviation of 6.5 hours. He measured the length of time his wife’s cell phone battery lasted on nine different occasions and calculated a mean of 24.1 with a standard deviation of 8.9. Construct and interpret a 95% confidence interval for the true difference in battery life between John’s cell phone and his wife’s cell phone. (10 points each)
12. Assume the population variances are the same

1. Assume the population variances are different

12. Students from two different schools took the same standardized test.

From school A, a random sample of 53 students had a mean score of 80. From school B, a random sample of 44 students had mean score of 84. Assume the population standard deviations are 9 for school A and 5 for school B. Construct and interpret a 90% confidence interval for the true difference between the mean test scores of the two schools. Also, what is the point estimate? (15 points)

13. A dietician wants to see how much weight a certain diet can help her 9 patients lose. She weighs each patient before and 45 days later. Her results are in the table. Construct and interpret a 98% confidence interval and calculate the paired differences for the true mean difference between the weights to determine the mean amount of weight lost by going on this diet (15 points).

14. A teacher wants to have his students in two different classes evaluate his teaching on a scale of 1-10 with 10 being excellent. The results of the first class with 18 students was a mean of 5.8 with a standard deviation of 1.2, and the second class with 15 students was a mean of 7.2 with a standard deviation of 1.5. Construct and interpret a 95% confidence interval to estimate a true difference between the two classes. Assume that the population variances are different (10 points).

15. For the data below, complete the following (20 points):

1. Draw a scatter plot

1. Estimate the correlation in words (positive, negative, or none)
2. Explain your estimation

1. Calculate the correlation coefficient (r-value)
2. Explain what the correlation coefficient (r) tells about the data

1. Calculate the coefficient of determination (r²)
2. Explain what the coefficient of determination tells about the data

1. Calculate the least-squares regression line (line of best fit)

1. Predict the bone density at age 56