a Suppose Alejandro studies a random sample of data on a cat

a. Suppose Alejandro studies a random sample of data on a categorical variable and calculates a 95% confidence interval for the population proportion to be (.846, .974). Determine what the sample proportion must have been, and explain why.

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b. Suppose Brad and Carly plan to collect separate random samples, with Brad using a sample size of 1500 and Carly using a sample size of 500. If Brad plans to construct a 90% confidence interval for the population proportion and Carly plans to construct a 99% confidence interval, who is more likely to obtain an interval that succeeds in capturing the population proportion? Explain.

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c. Suppose three students conduct a group project to estimate the proportion of students at their university who are from a different state. They take a random sample of students and find that 20% of their sample of students are from a different state. They then determine the following confidence intervals for the population proportion who are from a different state. One of these is a 90% confidence interval, one is a 99% confidence interval, and one is incorrect. Identify which is which. (In other words, write

Solution

Answe1

Ans:
a. p = (0.846+0.974)/2 = 0.91 (Ans.)

Answer 2

Brad, because his interval is 90% confident to contain the true proportion. Carly\'s is 99% confident to contain the true proportion.