Question

Read carefully through the following problems (Questions 5-8). Each problem is accompanied by a null and an alternative hypothesis, and each set of hypotheses includes at least one mistake. We would like you to identify what the mistake(s) is/are.

1. A claim is made that adults spend an average of $475 per year on birthday presents. A researcher believes this value is too low, and she sets out to gather data to test this claim. Her null and alternative hypotheses are below.

H_o: x = $475

H_a: x > $475

2. It is claimed that 52% of college students own an iPad. You believe a different proportion of college students own an iPad. Your null and alternative hypotheses are below.

H_o: p = 0.52

H_a:   p < 0.52

3. It is claimed that high school students across the country spend an average of 10.7 hours per week working at a part-time job. Teachers at one high school worry their students are spending too much time working at part-time jobs and not enough time studying. To determine if these students spend significantly more than 10.7 hours per week working at part-time jobs, they survey a random sample of 45 students. They find the sample average number of hours working at part-time jobs per week to be 12.5.   They plan to conduct a hypothesis test, and they begin with the following hypotheses:

H_o: µ = 12.5

H_a: µ < 12.5

4. Researchers claim that 240 seconds is the average amount of time people spend brushing their teeth per day. You think the true average is less than 240 seconds. You write out the following null and alternative hypotheses.

H_o: p = 120

H_a: p < 120

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 475
Alternative Hypothesis, Ha: μ < 475

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.52
Alternative Hypothesis, Ha: p ≠ 0.52

3)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10.7
Alternative Hypothesis, Ha: μ > 10.7

4)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 240
Alternative Hypothesis, Ha: μ < 240