Plug these values into the formula interval confidence interval

Solved Step by Step With Explanation- 90% CI for Mean Visits

Questions

b. With 90% confidence the population mean number of visits per week is between and visits.

c. If many groups of 211 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.

The formula for the confidence interval for the mean with a t-distribution is:

Confidence Interval = x̄ ± t * (s / √n)

t is the critical t-value for a 90% confidence interval with (n-1) degrees of freedom

You can find the critical t-value using a t-table or calculator. For a 90% confidence interval with 210 degrees of freedom (211 - 1), you can use a t-table or calculator to find the t-value. The critical t-value for a 90% confidence level is approximately 1.645.

c. If many groups of 211 randomly selected members are studied, about 90% of these confidence intervals will contain the true population mean number of visits per week, and about 10% will not contain the true population mean number of visits per week. This is because a 90% confidence level means that in the long run, you can expect approximately 90% of such intervals to contain the true population mean when taking random samples.