Question

A touristic destination is assessing the effectiveness of their business, both in terms of the true average of visitors and in the stability of the visits during a particular season.

For the previous charge, they select a random sample days of days with the premise that effectiveness should overcome the 93% of the room occupancy.

The records indicate a historic variance of 7.3 and the days selected show the following number of occupied rooms show the following:

78; 77; 76; 78; 77; 79; 77; 76; 75; 74; 77; 78; 76; 76; 76; 78; 78; 79; 75; 76; 77

1) Determine the necessary sample size if the total number of rooms of the hotel 80 and there are records that show as ordinary 93% occupancy, they would need for the estimation of the population proportion parameter with a margin of error less than 10%.

2) Determine the 98 % confidence interval for the true average for the occupied rooms.

3) Determine the 90 % Confidence interval for the variance of occupied rooms in the hotel

Answer 1

1. Assuming at 95% level of confidence,

To find sample size (n) such that

Margin of error = 0.1

2.

3. Here

sample variance

and sample size n = 21

a 90 % Confidence interval for the variance of occupied rooms in the hotel