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A statistics instructor believes that fewer 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 11 of them attended the midnight showing. At a 1% level of significance, an appropriate conclusion is:

User Eomeroff
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20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

User Rvector
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Answer: It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

Explanation:

Since we have given that

n = 84

x = 11

So,
\hat{p}=(x)/(n)=(11)/(84)=0.13

p = 0.20

So, hypothesis:


H_0:p=\hat{p}\\\\H_a:\hat{p}<p

so, test statistic value would be


z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.13-0.20}{\sqrt{(0.2* 0.8)/(84)}}\\\\z=-1.604

At 1% level of significance, critical value would be

z= 2.58

Since 2.58>-1.604

So, We will accept the null hypothesis.

Hence, It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

User Soumen Mukherjee
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