Create a problem statement about computing the length of confidence interval and determining the sample size

Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a sample proportion of 18 percent and a margin of error of 4 percent. What is the width of the confidence interval?

Suppose the length of a confidence interval is ten. If the point estimate is forty-five, what is the confidence interval? Suppose the margin of error of a confidence interval is six. If the point estimate is eighty, what is the confidence interval?

Suppose that Tom and Jerry determine confidence intervals using the same confidence level, based on the same sample proportion. Tom uses a larger sample size than Jerry. How will the midpoint and width of the confidence intervals compare? Same midpoint and same width   Same midpoint, Tom has a wider interval   Same midpoint, Jerry has a wider interval   Same width, Tom has a larger midpoint   Same width, Jerry has a larger midpoint   Tom has a larger midpoint, wider interval   Jerry has a larger midpoint, wider interval

Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means. Is the sampling distribution of the difference in sample means approximately normal? A) Yes, because Alicia selected a random sample. B) Yes, because for each brand it is reasonable to assume that the population size is greater than ten times its sample size. C) Yes, because the size of each sample is at least 30. D) No, because the distribution of Brand A shoes has outliers. E) No, because the shape of the population distribution is unknown.

In a survey of 813 human resource professionals concerning challenges they faced in the workplace, 321 said that employee retention was an important challenge and 194 said that employee satisfaction was an important challenge.  the 95% confidence interval estimate for the population proportion is

Why would manufacturers or businesses be interested in constructing a confidence interval for the population measure?  Would manufacturers or businesses want large or small margins of error?

What effect would increasing sample size have on a confidence interval?  What effect would decreasing sample size have on the margin of error?