Question

Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at college. A group of researchers at the Off-Campus Housing department want to estimate the mean monthly rent that unmarried students paid during winter 2018. During March 2018, they randomly sampled 314 students and found that on average, students paid $346 for rent with a standard deviation of $86. The plot of the sample data showed no extreme skewness or outliers. Calculate a 96% confidence interval estimate for the mean monthly rent of unmarried students in winter 2018.

What is a 96% confidence interval estimate for the mean monthly rent of BYU students in winter 2018?

State the name of the appropriate estimation procedure.

Describe the parameter of interest in the context of the problem.

Name the conditions for the procedure.

Explain how the above conditions are met.

Write down the confidence level and the t* critical value.

Calculate the margin of error for the interval to two decimal places​. Show your work.

Calculate the confidence interval to two decimal places​ and state it in interval form​.

Interpret your confidence interval in context. Do this by including these three parts in your conclusion: ● Level of confidence ● Parameter of interest in context ● The interval estimate.

FURTHER ANALYSIS

1. How would selecting a 90% level of confidence change the size of the calculated confidence interval? Explain or justify your answer by recalculating.

2. At a 95% level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of ± $25? Use σ = $86.  

3. Suppose that a second random sample of unmarried BYU students was conducted during March 2018. Using this data, the confidence interval was calculated to be ($340.65, $345.35). Rounded to two decimal places​, what is the margin of error for this confidence interval? Show your work.

Answer 1