## A lakefront resort is planning for its summer busy season. It wishes to estimate with 95% confidence the average number of nights each guest

Question

A lakefront resort is planning for its summer busy season. It wishes to estimate with 95% confidence the average number of nights each guest will stay for a consecutive visit. Using a sample of guests who stayed last year, the average number of nights per guest is calculated at 5 nights. The standard deviation of the sample is 1.5 nights. The size of the sample used is 120 guests and the resort desires a precision of plus or minus .5 nights. What is the standard error of the mean in the lakefront resort example? Within what range below can the resort expect with 95% confidence for the true population means to fall? Show the calculation; otherwise, the answer will not be accepted.

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4 days 2021-10-10T21:39:31+00:00 1 Answer 0 The 95% confidence interval would be given by (4.729;5.271)

Step-by-step explanation:

1) Previous concepts

A confidence interval is “a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval”.

The margin of error is the “range of values below and above the sample statistic in a confidence interval”.

The standard error of a statistic is “the standard deviation of its sampling distribution or an estimate of that standard deviation”

Normal distribution, is a “probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean”. represent the sample mean for the sample population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

The confidence interval for the mean is given by the following formula: (1)

We use the t distirbution for this case since we don’t know the population standard deviation .

Where the standard error is given by: And the margin of error would be given by: In order to calculate the critical value we need to find first the degrees of freedom, given by: Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. And we see that The standard error would be given by: Now we have everything in order to replace into formula (1) and calculate the interval:  So on this case the 95% confidence interval would be given by (4.729;5.271)