Elementary stats assignment help

8.1.4 Exercises for Section 8.1 Confidence Intervals for the Population Mean: Large Samples

1. We have a simple random sample of the systolic blood pressure (measured in mm Hg) of 20

individuals. The recorded readings are 120, 165, 133, 118, 110, 133, 125, 147, 89, 102, 111,

128, 140, 155, 156, 170, 131, 101, 112, and 104. What is the sample mean? What is the

standard error of the mean?

2. The standard deviation for the amount of time college students spend online per day is 5.5

hours. This number is based on a simple random sample of 36 college students. What is the

standard error of the mean?

3. Find the z* value for the following levels of confidence: a. 95% b. 80% c. 65%

4. Would a 95% confidence interval produce a smaller or larger confidence interval than a 65%?

Explain your answer.

Use the following to answer questions 5–12:

The amount of time (in minutes) it takes a simple random sample of 25 students in a basic

statistics class to finish the final exam are: 25, 60, 120, 130, 40, 45,60, 66, 101, 90, 88, 31, 60,

62, 26, 20, 100, 85, 90, and 23

5. What is the sample mean? 6. What is the standard deviation?

7. What is the standard error of the mean?

8. What is the margin of error?

9. Provide an 80% confidence interval for the mean.

10. Provide a 99% confidence interval for the mean. Was this interval larger or smaller than the

interval you calculated in exercise 9? Why does that make sense?

11. Provide ways to reduce the margin of error in exercise 8.

12. What sample size would you need to have a margin of error less than 5 based on an 80%

confidence interval?

1. If you have an SRS with measurements on five individuals, how many degrees of freedom

are there for the critical value of the t-distribution?

2. For small samples sizes, is the t-distribution skewed or symmetric? Provide a graph of such a

t-distribution for this situation.

3. Is the t-distribution a continuous or discrete distribution? 4. Provide the critical values for the

t-distribution based on the following information: a. 95% confidence level and a sample size of

9. b. Alpha level of 0.01 and sample size of 12.

4. Provide the critical values for the t-distribution based on the following information: a. 95%

confidence level and a sample size of 9. b. Alpha level of 0.01 and sample size of 12.

c. 80% confidence level and a sample size of 15.

5. When the sample size is large, the t-distribution is approximately what distribution?

6. The average number of movies that an SRS of 16 people watch per month is 10. Find an

80% confidence interval based on a sample standard deviation of 2.

7. Assume you have an SRS of 100 individuals in which the distribution of their height (in

inches) is approximately normal. Would you base a confidence interval of the mean on the

t-distribution or normal distribution? Explain your answer.

8. Are confidence intervals for the mean used to provide a range of values for the sample mean

or the population mean? Why?

1. How many parameters are needed to draw a chi-square distribution? Decide on a value for

these parameters and draw a chi-square distribution of your choice.

2. Determine the critical values for a chi-square distribution based on an alpha level of 0.01 with

the following factors:

a. Degrees of freedom of 10. b. Degrees of freedom of 1. c. A sample size of 50.

3. Compute the critical values for a chi-square distribution for the lower bound and upper

bounds of a confidence interval for the variance and standard deviation based on the following

levels of confidence with a sample size of 20.

a. 90% b. 65% c. 80%

4. The sample standard deviation for the amount of time a random sample of 18 students sleeps

per night is six hours. Provide a confidence interval for the population variance and standard

deviation.

5. Is the confidence interval you computed in the previous exercise symmetric around the

estimate? Explain why or why not.

6. The 95% confidence interval for the population variance of the amount of money students

spend each week in U.S. dollars is (20.38, 80.87). What is the 95% confidence interval for the

population standard deviation?

7. Provide some sample statistics.

8. What distribution would be used to compute a confidence interval for the standard deviation?

Provide the distribution along with its appropriate parameters.

9. What is the 95% confidence interval for the standard deviation? 10. What is the 80%

confidence interval for the variance?

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