Question

Kennebunkport, Maine, is a popular tourist town, but businesses suffer during the winter months, especially January. The mean hotel room occupation rate per day, a measure of tourist activity, is 23.1% during winter months. A new advertising campaign was launched to attract more tourists to this town during the winter. Following the campaign, a random sample of nine winter days was selected. The mean hotel room occupation rate was

x = 24.7%

and

s = 2.1%.

Is there any evidence to suggest the mean hotel room occupation rate has increased? Assume normality and use

α = 0.01.

a) Give the value of the appropriate t_{α, n − 1} or t_{α/2, n − 1}. (Round your answer to four decimal places.)

b) Calculate the test statistic. (Round your answer to four decimal places.)

t =

Answer 1

a)

H0: <= 23.1%

Ha: > 23.1%

This is one tailed test.

For unknown population standard deviation, we use t test.

t,n-1 = 2.8965

b)

Test statistics

t = ( - ) / (S / sqrt(n) )

= (24.7 - 23.1) / (2.1 / sqrt(9) )

= 2.2857

Since test statistics < 2.8965. do not reject H0.