Question

A travel association claims that the mean daily food cost for two adults traveling together on vacation in San Francisco is $110. A random sample of 14 groups of adults is used to conduct a hypothesis test to show that the mean daily food is greater than 110. Using the mean and sample standard deviation from this sample, the test statistic was calculated to be 1.76. The corresponding p-value of this test is:

a. 0.05 < p-value < 0.10

b. 0.10 < p-value < 0.20

c. 0.0392

d. 0.0784

Answer 1

Solution :-

Given :- A random sample of 14 groups of adults is used to conduct a hypothesis test to show that the mean daily food is greater than 110.

The above statement indicate the given test is right tailed test.

Hypothesis :-

Ho : u = 110

H1 : u > 110 ( Right tailed test.)

test statistic ( t ) = 1.76 ( Given )

Sample size ( n ) = 14 ( Given )

df = n - 1

df = 14 - 1

df = 13

Therefore by using P value approach, at t = 1.76 and df = 13 for right tailed test.

P ( t > 1.72 ) = 0.0510

P value = 0.0510

P value = 0.0510 ranges from,

0.05 < P Value < 0.10

option ' a ' is correct.