Answer the following True or False:
Last year, 30 percent of Americans travelled out of town for their
Thanksgiving dinner. A hypothesis test was performed to see if that
percent has declined this year (H0: p = 0.30,
Ha: p < 0.30). The level of significance of 0.05 was
used and the p-value was found to be 0.48. Since p > αα , it can
be concluded that the percent of Americans who travelled out of
town for Thanksgiving has not declined this year.
Solution :
This is the left tailed test .
The null and alternative hypothesis is
H0 : p = 0.30
Ha : p < 0.30
n =30
= 0.48
P0 = 0.30
1 - P0 = 1 - 0.30 =0.70
Test statistic = z
= - P0 / [P0 * (1 - P0 ) / n]
= 0.48 - 0.30/ [(0.30*0.70) /30 ]
= 2.15
Test statistic = z =2.15
P(z < 2.15) = 0.9842
P-value = 0.9842
= 0.05
P-value >
0.9842 > 0.05
Fail to reject the null hypothesis .
There is not sufficient it can be concluded that the percent of Americans who travelled out of town for Thanksgiving has not declined this year.
A ) True
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