Math Problem Solver

The authors of a research article used a paired samples t test to reach the conclusion that male college students tend to over-report both weight and height. This conclusion was based on a sample of 635 male college students selected from eight different universities. The sample mean difference between the reported weight and actual measured weight was 1.1 pounds and the standard deviation of the differences was 5.76 pounds. For purposes of this exercise, you can assume that the sample was representative of male college students.

A button hyperlink to the SALT program that reads: Use SALT.

(a)

Carry out a hypothesis test to determine if there is a significant difference in the mean reported weight and the mean actual weight for male college students. (Use

𝛼 = 0.05.

Use

𝜇d = 𝜇reported − 𝜇actual.)

State the appropriate null and alternative hypotheses.

H0: 𝜇d ≠ 0

Ha: 𝜇d = 0

H0: 𝜇d > 0

Ha: 𝜇d = 0

H0: 𝜇d = 0

Ha: 𝜇d < 0

H0: 𝜇d = 0

Ha: 𝜇d > 0

H0: 𝜇d = 0

Ha: 𝜇d ≠ 0

Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)

t =

P-value =

State the conclusion in the problem context.

We reject H0. There is not a significant difference in the mean reported weight and the mean actual weight for male college students.

We fail to reject H0. There is not a significant difference in the mean reported weight and the mean actual weight for male college students.

We fail to reject H0. There is a significant difference in the mean reported weight and the mean actual weight for male college students.

We reject H0. There is a significant difference in the mean reported weight and the mean actual weight for male college students.

(b)

For height, the mean difference between the reported height and actual measured height was 0.6 inches and the standard deviation of the differences was 0.9 inches. Carry out a hypothesis test to determine if there is a significant difference in the mean reported height and the mean actual height for male college students. (Use

𝛼 = 0.05.

Use

𝜇d = 𝜇reported − 𝜇actual.)

State the appropriate null and alternative hypotheses.

H0: 𝜇d ≠ 0

Ha: 𝜇d = 0

H0: 𝜇d > 0

Ha: 𝜇d = 0

H0: 𝜇d = 0

Ha: 𝜇d < 0

H0: 𝜇d = 0

Ha: 𝜇d > 0

H0: 𝜇d = 0

Ha: 𝜇d ≠ 0

Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)

t =

P-value =

State the conclusion in the problem context.

We reject H0. There is a significant difference in the mean reported height and the mean actual height for male college students.

We reject H0. There is not a significant difference in the mean reported height and the mean actual height for male college students.

We fail to reject H0. There is not a significant difference in the mean reported height and the mean actual height for male college students.

We fail to reject H0. There is a significant difference in the mean reported height and the mean actual height for male college students.

(c)

Do the conclusions reached in the hypothesis tests of parts (a) and (b) support the given conclusion that male college students tend to over-report both height and weight? Explain.

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resulted in rejecting the null hypothesis. Additionally, the t test statistics are

---Select---

, which tells us that the population mean differences are likely to be

---Select---

for reported value minus actual value. As such, we

---Select---

convincing evidence that male college students tend to over-report both height and weight.