1. Find the point estimate of the population mean and the margin of error for a 90% confidence interval for the following drive times (in minutes) for commuters to a college.
35 40 47 22 17 19 36 44 65
55 22 23 16 46 44 38 29 22
37 16 8 15 27 41 45 17 11
45 63 17 28 19 64 55 53 50
2. Use the results from the above data (#1) and determine the minimum survey size that is necessary to be 95% confident that the sample mean drive time is within 10 minutes of the actual mean commuting time.
3. In a random sample of 35 tractors, the annual cost of maintenance was $4,425 and the standard deviation was $775. Construct a 90% confidence interval for this. Assume the annual maintenance costs are normally distributed.
4. The following data represents the number of points scored by players on a high school basketball team this season.
Player 1 68 Player 6 128
Player 2 82 Player 7 66
Player 3 145 Player 8 54
Player 4 111 Player 9 221
Player 5 97 Player 10 99
a. Find the sample mean and the sample standard deviation.
b. Construct a 90% confidence interval for the population mean and interpret the results. Assume the population of the data set is normally distributed.
5. For the following statements, state the null and alternative hypotheses and identify which represents the claim. Determine when a type I or type II error occurs for a hypothesis test of the claim. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and explain your reasoning. Explain how you should interpret a decision that rejects the null hypothesis. Explain how you would interpret a decision that fails to reject the null hypothesis.
a. It is reported that the number of residents in Wisconsin who support plans to recall the governor is 48%.
b. An Amish bakery store states that the average shelf life of their fresh baked goods is seven days.
c. A soda manufacturer states that the average number of calories in the regular soda is less than 150 calories per serving.
6. The census figures show that the average income for a family in a rural region is approximately $34,860 per year. A random sample has a mean income of $33,566 per year, with a standard deviation of $1,245. At a sig. level of .0.01 is there enough evidence to reject the claim? Explain.
7. An advertising firm claims that the average expenditure for advertising for their customers is at least $12,500 per year. You want to test this claim, so you randomly select 10 of their customers. The results are listed below. At a sig. level of .01 can you reject this claim? Explain.
13,445 11,220 10,157 13,217 9,990
12,125 10,116 14,350 13,590 12,100
8. Find the critical value(s) for the indicated test for a population variance, sample size, and sig. level.
a. Right-tailed test - Sample Size (25), Significance (.05)
b. Two-tailed test - Sample Size (11), Significance (.01)
c. Two-tailed test - Sample size (66), Significance (.10)
d. Left-tailed test - Sample Size (18), Significance (.05)
9. The employees in a grocery store are handing out samples of a certain brand of Pizza. This is the pizza company's way of determining whether people like the brand of pizza and would prefer it over other brands. Do you think this type of sampling is representative of the population? Explain. Identify possible flaws or biases in this study.
10. Classify the following as independent or dependent and explain your answer.
a. Sample 1 - The males in the class
Sample 2 - The females in the class
b. Sample 1 - Blood Pressure of fifteen people in a nursing home
c. Sample 2 - Blood pressure of the same fifteen people one week later
11. A researcher claims that taking a protein supplement as part of a weight gainer program for athletes will help them gain muscle weight. The weights in pounds of 10 athletes are listed below before and after using the protein supplement. At a sig. of .05 can you conclude that this supplement helps the athletes gain weight?
12. Technology: A math teacher claims that the average final exam scores for the seventh grade boys and girls are equal. The average score for 10 randomly selected boys is 87 with a standard deviation of 11. The average score for 10 randomly selected girls is 89 with a standard deviation of 12. State the null and alternate hypotheses. At a sig. of .05 can you reject the teacher's claim? Assume normal distribution and equal variances. Please use Excel for your calculations. What is your analysis?