Question

A statistics instructor believes that more than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 21 attended the midnight showing. The test value is equal to:

a) 0.25
b) 1.5
c) 2.5
d) 4.0

Answer 1

The computed test statistic for the hypothesis test regarding the proportion of students who attended the midnight showing is approximately 1.145. The closest value from the given options is 1.5.

Step-by-step explanation:

The question involves calculating the test statistic for a hypothesis test regarding a proportion. The statistics instructor believes that more than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. Upon surveying 84 students, the instructor found that 21 students attended the midnight showing.

To determine the test value (test statistic), we use the formula for the test statistic for a proportion, which is:

Z = (p - P0) / sqrt(P0(1-P0)/n)

Where:

p is the sample proportion (21/84)

P0 is the hypothesized population proportion (0.20)

n is the sample size (84)

Calculating this gives us:

p = 21/84 = 0.25

Z = (0.25 - 0.20) / sqrt(0.20(1-0.20)/84)

Z = 0.05 / sqrt(0.20*0.80/84)

Z = 0.05 / sqrt(0.16/84)

Z = 0.05 / sqrt(0.00190476)

Z = 0.05 / 0.04364279

Z ≈ 1.145

The closest value to this calculated Z score from the options provided is option (b) 1.5.