Week 8 – Assignment: Construct Confidence Intervals and Statistical TestsInstructionsFor 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 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 , what is the correct critical value z*?
b) To construct a 99% confidence interval for a population mean , 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: = 10 against the alternate H1: 10. A simple random sample of 35 observations from a normal population are used for a test. What values of the z statistic are statistically significant at the = 0.05 level?
Describe the four-step process for tests of significance according to the textbook.
Part 2A 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.
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