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

The hypothesis the statistician wants to test is d) H0: μ = 75 vs. Ha: μ > 75, as the statistician is looking for evidence that the true average score is higher than the hypothesized mean of 75%. So the correct option is d.

Step-by-step explanation:

The hypothesis the statistician wants to test is d) H0: μ = 75 vs. Ha: μ > 75. This is because the null hypothesis (H0) typically represents the status quo or the claim to be tested, which in this case is that students score at least 75% on the final exam. The alternative hypothesis (Ha), on the other hand, is what the statistician suspects might be true instead of H0. Since the statistician is testing the hypothesis that the students score at least 75%, this suggests that they are looking for evidence of a score higher than 75%, making this a one-tailed test.

The null hypothesis is stated as equality (H0: μ = 75), and the alternative hypothesis is that the true mean score is greater than 75% (Ha: μ > 75). An average score of 78% by the sample does not establish the alternative hypothesis but indicates that leads the statistician to test if the true average score could indeed be greater than 75%.

Answer 2

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