Calculate the related confidence interval for the difference in average daily hotel room rates and explain in a sentence what information this gives.

The easiest way to calculate the confidence interval would be by using Microsoft’s excel spreadsheet. The syntax or formula for doing this is as follows;

=CONFIDENCE (alpha, standard deviation, size)

Alpha represents the significance level. In this case, an assumption will be made as to the value because the significance level has not been indicated

Standard deviation represents the standard deviation for the population which is a known figure. In the data provided, the symbol,...

The easiest way to calculate the confidence interval would be by using Microsoft’s excel spreadsheet. The syntax or formula for doing this is as follows;

=CONFIDENCE (alpha, standard deviation, size)

Alpha represents the significance level. In this case, an assumption will be made as to the value because the significance level has not been indicated

Standard deviation represents the standard deviation for the population which is a known figure. In the data provided, the symbol, S d the standard deviation.

Size represents the sample size. In the data provided, the symbol, n d the size.

Confidence intervals for the two areas (Christchurch and Auckland) will be calculated using excel to answer the first part of the question as seen below.

Alpha, in this case, will be assumed to be 0.05.

Christchurch: =CONFIDENCE (0.05, 11.05, 22) = 4.617416

Auckland: =CONFIDENCE (0.05, 12.34, 20) = 5.408144

The results show that the confidence interval between the two areas is different.

This can further be represented and explained as follows;

Christchurch: 112.42 +or- 4.617416 where 112.42 is the average hotel room rate in Christchurch according to the data provided. Thus, 117.037416 forms the upper bound of the interval and 107.802584 forms the lower bound of the interval.

For any population mean, μ0, in this interval, the probability of obtaining a sample mean further from μ0 than 112.42 is more than 0.05. Likewise, for any population mean, μ0, outside this interval, the probability of obtaining a sample mean further from μ0 than 30 is less than 0.05.

Auckland: 122.78 +or- 5.408144 where 122.78 is the average hotel room rate in Christchurch according to the data provided. Thus, 128.188144 forms the upper bound of the interval and 117.371856 forms the lower bound of the interval.

For any population mean, μ0, in this interval, the probability of obtaining a sample mean further from μ0 than 122.78 is more than 0.05. Likewise, for any population mean, μ0, outside this interval, the probability of obtaining a sample mean further from μ0 than 30 is less than 0.05.