Question

A statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the students on the exam was 78%. The hypothesis the statistician wants to test is_________.
a) H0: μ = 75 vs. Ha: μ > 78
b) H0: μ = 75 vs. Ha: μ < 75
c) H0: μ = 75 vs. Ha: μ = 78
d) H0: μ = 75 vs. Ha: μ > 75

Answer 1

Answer:

The hypothesis the statistician wants to test is $H_0$ : $\mu$ = 75 vs $H_a$ : $\mu$ > 75.

Step-by-step explanation:

We are given that a statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the students on the exam was 78%.

Firstly, as we know that testing is always done on the population data.

So, let $\mu$ = average students score on the final exam in an introductory statistics course

The hypothesis situation that the statistician wants to test is given by;

Null Hypothesis, $H_0$ : $\mu$ = 75  {means that the average students score on the final exam in an introductory statistics course is equal to 75%}

Alternate Hypothesis, $H_a$ : $\mu$ > 75  {means that the average students score on the final exam in an introductory statistics course is greater than 75%}

So, from the options given to us, the appropriate option is ;

Option (d) : $H_0$ : $\mu$ = 75 vs $H_a$ : $\mu$ > 75