Question

A statistics instructor believes that fewer than $20\%$Evergreen Valley College $\left(EVC\right)$students attended the opening night midnight showing of the latest Harry Potter movie. She surveys $84$her students and finds that $11$attended the midnight showing. An appropriate alternative hypothesis is:

1. $p=0.20$
2. localid="1650019309031" $p>0.20$
3. $p<0.20$
4. $p\le 0.20$

Short answer

The alternative hypothesis is:$H_a:p>0.2.$

Step-by-step solution

Introduction

The one-sample t-test is a statistical hypothesis test that is used to see if an unknown population mean differs from a given value.

The relevant null and alternative hypotheses must be stated first in a hypothesis test.

When completing the test, the second step is to consider the statistical assumptions made about the sample. The relevant test statistic is then shown, and its distribution is calculated using the null hypothesis assumptions.

The null hypothesis states that there is no difference between a proportion and the proportion of the population.

The alternative hypothesis is a population assertion that contradicts to$H_0$

Explanation Part a

Note that $H_0$always has a symbol with an equal in it and $H_a$never has a symbol with an equal in it.

We know that a statistics instructor believes that fewer than $20\%$students attended the opening night midnight showing of the latest Harry Potter movie.

So, the null hypothesis is:

$H_0:p\ge 0.2$

Therefore, option a is not correct.

Explanation Part b

The null hypothesis states that there is no difference between a proportion and the proportion of the population. The alternative hypothesis is a population assertion that contradicts$H_0.$

As $20\%$students attend the opening show of harry potter movie, the null hypothesis is:

$H_0:p\ge 0.2$

and alternative hypothesis is:

$H_a:p>0.2$

Explanation Part c

We know that a statistics instructor believes that fewer than $20\%$students attended the opening night midnight showing of the latest Harry Potter movie.

So, the null hypothesis is:

$H_0:p\ge 0.2$

Then, the alternative hypothesis is:

$H_a:p>0.2$

Therefore, option c is not correct.

Explanation Part d

We know that a statistics instructor believes that fewer than $20\%$students attended the opening night midnight showing of the latest Harry Potter movie.

So, the null hypothesis is:

$H_0:p\ge 0.2$

Therefore, option d is not correct.