Question

1. a national student life organization claims that 16% of college students choose not to take part in any extracurricular activities during their time in college. a university administrator disagrees with this claim. the administrator surveys a large random sample of college students and finds that the percentage of students in the sample who have chosen not to participate in extracurricular activities lies exactly one and a half standard errors above 16%. based on this information, what can we say about the resulting p - value for this hypothesis test?

a. the p - value is between 0.01 and 0.05.
b. the p - value is between 0.05 and 0.10.
c. the p - value is smaller than 0.01.
d. the p - value is larger than 0.10.
e. the p - value cannot be determined based on the given information.

Explanation:

Step1: Determine the type of test

Since the university administrator disagrees with the claim (not specifying a direction like "higher" or "lower" only that it's different), this is a two - tailed test.

Step2: Use the standard normal distribution property

For a two - tailed test, if \(z = 1.5\), the \(P-\)value is \(2\times(1 - P(Z<1.5))\).
From the standard normal table, \(P(Z < 1.5)=0.9332\).
Then \(P-\)value \(=2\times(1 - 0.9332)=2\times0.0668 = 0.1336\)

Answer:

D. The \(P-\)value is larger than \(0.10\)