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 tα, n − 1 or tα/2, n − 1. (Round your answer to four decimal places.)
b) Calculate the test statistic. (Round your answer to four decimal places.)
t =
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.
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