Question

3: A statistics instructor believes that fewer than 20% of Evergreen Valley College students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing.

Let ? = proportion of Evergreen Valley College students that attended the midnight showing.

A: State the Null and Alternate Hypotheses.
B: Determine the test statistic for the sample.
C: Find the p-value.
D: At a significance level of ? = 0.01, do you reject or fail to reject the null hypothesis?

E: Write the appropriate conclusion about the claim / belief.

Answer 1

A)

H0: p >= 0.20

Ha: p < 0.20

B)

Sample proportion = 11 / 84 = 0.1310

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.1310 - 0.20) / sqrt(0.20 ( 1 - 0.20) / 84 )

= -1.58

c)

p-value = P(Z < z)

= P(Z < -1.58)

= 0.0571

D)

Since p-value > 0.01, Fail to reject the null hypothesis.

E)

We do not have sufficient evidence to support the claim that ewer than 20% of Evergreen Valley College  

students attended the opening night midnight showing of the latest Harry Potter movie.