Statistics Homework

7. The lifetime of a certain brand of battery is known to have a standard deviation of 11.5 hours. Suppose that a random sample of 90 such batteries has a mean lifetime of 36.8 hours. Based on this sample, find a 90% confidence interval for the true mean lifetime of all batteries of this brand. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

a. What is the lower limit of the 90% confidence interval?

b. What is the upper limit of the 90% confidence interval?

8. The standard deviation of test scores on a certain achievement test is 11.5. A random sample of 90 scores on this test had a mean of 73.2. Based on this sample, find a 99% confidence interval for the true mean of all scores. Then complete the table below

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

a. What is the lower limit of the 95% confidence interval?

b. What is the upper limit of the 95% confidence interval?

9. A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage, µ, of cares rented in the U.S. over the past year. The consumer group plans to choose a random sample of monthly U.S. rental car mileage and then estimate µ, using the mean of the sample.

Using the value 700 miles per month as the standard deviation of monthly U.S. rental car mileage from the past year, what is the minimum sample size needed in order for the consumer group to be 99% confident that is estimate is within 175 miles per month of µ?

Carry your intermediate computations to at least three decimals places. Write your answer as a whole number and make that it is minimum whole number that satisfies the requirements? Answers

10. Many college graduates who are employed full-time have longer than 40-hour work weeks, suppose that we wish to estimate the mean number of hours, µ, worked per week by college graduates employed full-time. We will choose a random sample of college graduates employed full-time and use the mean of this sample to estimate µ. Assuming that the standard deviation of the number of hours worked by college graduates is 6.10 hours per week, what is the minimum sample size needed in order for us to be 95% confident that our estimate is within 1.2 hours per week of µ?

Carry your intermediate computations to at least three decimals places. Write your answer as a whole number and make that it is minimum whole number that satisfies the requirements? Answers

11. Use the calculator provided to solve the following problems

a. Consider a t distribution with 7 degrees of freedom. Compute P (t ≥ -1.94) Round your answer to at least three decimals places

b. Consider a t distribution with 15 degrees of freedom. Find the value of c such that P (-c < t< c) = 0.90. Round your answer to at least three decimal places.

12. Use the calculator provided to solve the following problems.

a. Consider a t distribution with 8 degrees of freedom. Compute P (-1.54 < t< 1.54). Round your answer to at least three decimals places.

b. Consider a t distribution with 25 degrees of freedom. Find the value of c such that P (t ≤ c) = 0.10. Round your answer to at least three decimals places.

13. Recorded here are the germination times (in days) for eighteen randomly chosen seeds of a new type of bean:

21, 11, 15, 21, 12, 11, 13, 10, 17, 20, 16, 15, 21, 12, 20,11, 16, 17

Assuming that germination times are normally distributed, find a 90% confidence interval for the mean germination time for all beans of this type. The complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

a. What is the lower limit of the confidence interval?

b. What is the upper limit of the confidence interval?

14. A researcher collected sample data for 17 women ages 18 to 24. The sample had a mean serum cholesterol level (measured in mg/100 ml) of 192.1, with a standard deviation of 8.1. Assuming that serum cholesterol levels for women ages 18 to 24 are normally distributed, find a 95% confidence interval for the mean serum cholesterol level of all women in this age group. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

a. What is the lower limit of the confidence interval?

b. What is the upper limit of the confidence interval?

15. After the premiere of the new comedy Bumblebee, moviegoers were asked in a quick poll whether they liked the movie. Out of 20, adults, all but 6 said they liked the movie, whereas out of 100 teenagers, all but 43 said they liked the movie.

Fill in the blanks of the statement below to make the statement the most reasonable possible

At the movie premiere, ______moviegoers liked the movie more because only _____% disliked the movie, where as ______% of the _______moviegoers disliked the movie.

16. In a recent study, 20 males used a new weight loos supplement, and all but 6 of them experienced weight loss after two weeks. In the same study, 100 females used the same supplement, and all but 46 of them experienced weight loss after two weeks.

Fill in the blanks of the statement below to make the statement the most reasonable possible

The new weight loss supplement was more effective on ______ in the study because only ____% of them failed to lose weight after two weeks, whereas _______% of the _________ failed to lose weight after two weeks.

17. From a large number of actuarial exams scores, a random sample of 200 scores is selected, and it is found that 136 of these 200 are passing scores, based on this sample, find a 95% confidence interval for the proportion of all scores that are passing.

Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

a. What is the lower limit of the 95% confidence interval?

b. What is the upper limit of the 95% confidence interval?

18. A sociologist is studying the prevalence of crime in one major city. In a sample of 225 randomly selected, 56 say that they have been victimized by a criminal. Based on this sample, construct a 90% confidence interval for the proportion of all residents in this city who have been victimized by a criminal. The complete the table below

Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

a. What is the lower limit of the 90% confidence interval?

b. What is the upper limit of the 90% confidence interval?

19. You would like to estimate the mean price of milk per gallon in your city. You select a random sample of prices from different stores. The sample has a mean of 3.51 dollars and a standard deviation of 0.29 dollars. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about population mean.

(In the table Z, refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution)

Sampling Scenario	Z	t	Could use either Z or t	unclear
1. The sample has size 95, and it is from a non-normally distributed population with known standard deviation of 0.25
2. The sample has size 80, and it is from a non-normally distributed population.
3. The sample has size 17, and it is from a population with a distribution about which we know very little
4. The sample has size 11, and it is from a normally distributed population with a known standard deviation of 0.25.
5. The sample has size 12, and it is from a normally distributed population with unknown standard deviation.

20. Suppose that we want to estimate the mean score on a nationwide examination in biology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 483 and a standard deviation of 80. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

(In the table, Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution.

Sampling Scenario	Z	t	Could use either Z or t	unclear
1. The sample has size 12, and it is from a normally distributed population with a known standard deviation of 75
2. The sample has size 15, and it is from a normally distributed population with unknown standard deviation.
3. The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 75.
4. The sample has size 20, and it is from a population with a distribution about which we know very little
5. The sample has size 80, and it is from a non-normally distributed population