Construct Confidence Intervals and Statistical Tests Week 8 – Assignment:

Construct Confidence Intervals and Statistical Tests

# Construct Confidence Intervals and Statistical Tests Instructions

For this task, write a paper using the following structure:

Begin with a one or two-paragraph introduction that summarizes the meaning of the reading material.

Answer all of the questions included in Parts 1 and 2 below. Be sure to answer questions using complete sentences and show all the work in your calculations.

Provide a written conclusion, when appropriate, for the problem that you are addressing.

Include an essay section in your paper, which is described in Part 3 below.

Use the last part of your paper to include a paragraph or two that explains the information that you learned in the assignment. Support your paper with at least two references.

Part 1

Explain the difference between a 95% confidence interval and a 99% confidence interval in terms of probability.

- a) To construct a 95% confidence interval for a population mean µ, what is the correct critical value z*?
- b) To construct a 99% confidence interval for a population mean µ, what is the correct critical value z*?

Explain what the margin of error is and how to calculate it.

A survey of a group of students at a certain college, we call College ABC, asked: “About how many hours do you study in a week?” The mean response of the 400 students is 15.8 hours. Suppose that the study time distribution of the population is known to be normal with a standard deviation of 8.5 hours. Use the survey results to construct a 95% confidence interval for the mean study time at the College ABC.

Explain the difference between a null hypothesis and an alternative hypothesis.

Suppose that you are testing a null hypothesis H0: µ = 10 against the alternative H1: µ ≠ 10. A simple random sample of 35 observations from a normal population is used for a test. What values of the z statistic are statistically significant at the α = 0.05 level?

Describe the four-step process for tests of significance according to the textbook.

Part 2

A study of a group of 40 male league bowlers chosen at random had an average score was 176. It is known that the standard deviation of the population is 9.

- a) Construct the 95% confidence interval for the mean score of all league bowlers.
- b) Construct the 95% confidence interval for the mean score of all league bowlers assuming that a sample of size 100 is used instead of 40, and the same mean and standard deviation occur.
- c) Give the margin of error for each interval.
- d) Explain why one confidence interval is larger than the other.

There are 100 apartments in a certain a San Francisco apartment building. The owner of the building wants to estimate the mean number of people living in an apartment. The owner draws a random sample of 40 apartments in the building. The number of people living in each apartment is as follows:

1 2 1 2 3 1 3 4 3 1

2 2 1 2 2 2 1 3 2 3

2 3 1 2 3 3 2 4 5 2

3 2 2 3 1 1 2 2 1 2

- a) Compute the sample mean and sample standard deviation.
- b) Use the results from part (a) to construct a 95% confidence interval.

A doctor wishes to estimate the birth weights of infants. How large a sample must the doctor select if she desires to be 99% confident that the true population means is at most 6 ounces away from the mean of the sample? Assume the standard deviation is 8 ounces. Hint: The margin of error should be at most 6.

In Problem 4 of Part 1, a class survey of 400 students was given in which students at College ABC claimed to study an average of 15.8 hours per week. Consider these students as a simple random sample from the particular population of College ABC students. We want to investigate the question: Does the survey provide good evidence that students study more than 15 hours per week on average? Assume the population of hours studied is normal with a standard deviation of 4.

Before working out this problem, it will help to look over the webpage, Hypothesis tests for means, http://stattrek.com/hypothesis-test/mean.aspx?Tutorial=AP

- a) State the null and alternate hypothesis in terms of the mean study time in hours for the population.
- b) Is this a one-tailed test or two-tailed test?
- c) Determine the value of the test statistic.
- d) Sketch a normal shape curve and identify the test statistic.
- e) Indicate the p-value of the test. Use the standard normal table. Shade the area under the normal curve corresponding to the p-value. You can also use the website cited above to do this.
- f) State your conclusion to the statistical problem in terms of the null hypothesis, and your conclusion to the practical problem.

Length: 5 – 7 pages

References: Include a minimum of two scholarly peer-reviewed resources.

Upload your document and click the Submit to Dropbox button.

External Resource (S): Books and Resources for this Week

- Statistics in Practice

Moore, D.S., Notz, W.I., & Fligner, M.A. (2015). Statistics in practice. New York, NY: W.H. Freeman.

Read Chapters 16 and 17

- StatTrek.Com. (2016). Hypothesis tests for means.

https://stattrek.com/hypothesis-test/mean.aspx?Tutorial=AP

- BUS-7200_Grading_Rubrics

Supplemental (External) Resource