Question

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 (H_{0}: p = 0.30,
H_{a}: 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.

- A)true
- B) false

Answer #1

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.

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