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A travel agent is interested in the average price of a hotel room during the summer in a resort community. The agent randomly selects 18 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 $135 with a standard deviation of $25. 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 99% confidence. Round the endpoints to two decimal places, if necessary.

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The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 ).

What is the confidence interval of an average?

One method of determining the actual population mean is by using a confidence interval for the mean. A confidence interval provides a lower estimate and an upper estimate rather than just the mean.

A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.

x = mean;

99% confidence interval for μ is

(x - t * S) /√n  <  μ <( x + t * S) /√n;

(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;

14.74<  μ< 48.89;

99% CI is ( 14.74, 48.89 ) ;

critical value at 0.01 significance level with 17 df = 2.898

To learn more about confidence interval refer :

https://brainly.com/question/14825274

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