Question

A travel agent is interested in the average price of a hotel room during the summer in a resort community. The agent randomly selects 17

hotels from the community and determines the price of a regular room with a king size bed. The average price of the room for the sample was $105
with a standard deviation of $40
. Assume the prices are normally distributed. Construct an interval to estimate the true average price of a regular room with a king size bed in the resort community with 95%
confidence. Round the endpoints to two decimal places, if necessary.

Answer 1

a confidence interval to estimate the true average price of a regular room with a king size bed in the resort community with 95% confidence is ($103.88, $106.12), we can use the formula: Confidence Interval = Sample Mean ± (Critical Value × Standard Error).

Step-by-step explanation:

To construct a confidence interval to estimate the true average price of a regular room with a king size bed in the resort community with 95% confidence, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value × Standard Error)

First, we need to find the critical value using a t-distribution with 16 degrees of freedom (n - 1). From the t-distribution table, the critical value for a 95% confidence level is approximately 2.131.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / sqrt(n)

Given that the sample mean is $105, the standard deviation is $40, and the sample size is 17, the standard error is:

Standard Error = $40 / sqrt(17)

= $9.68

Substituting the values into the confidence interval formula:

Confidence Interval = $105 ± (2.131 × $9.68)

Rounding the endpoints to two decimal places:

Confidence Interval = ($103.88, $106.12)