Question

Researchers want to test the effect of the Paleo diet. They randomly divided 500 volunteers into two equal-sized groups (of 250 each). One group spent 6 months on the Paleo diet. The other group received a pamphlet about controlling portion sizes. Randomized treatment assignment was performed, and at the beginning of the study, the average difference in weights between the two groups was about 0. After the study, the Paleo group had lost on average 7 pounds with a standard deviation of 20 pounds while the control group had lost on average 5 pounds with a standard deviation of 12 pounds.

State the null and alternative hypothesis.

Select one:

a. H_{0}: μμ_{P} - μμ_{C} = 0;
H_{A}: μμ_{P} - μμ_{C} ≠≠ 0

b. H_{0}: μμ_{P} - μμ_{C} = 0;
H_{A}: μμ_{P} > μμ_{C}

c. H_{0}: μμ_{P} - μμ_{C} = 0;
H_{A}: μμ_{P} < μμ_{C}

d. All of these are valid

Compute the standard error (SE)

Select one:

a. 1.475127

b. 2.176

c. 4.734976

d. 1.043

Compute the *Z* score

Select one:

a. 1.36

b. 0.9191

c. 0.4224

d. 1.9175

Compute the *p-*value.

Select one:

a. 0.1738

b. 0.9131

c. 0.0869

d. 1.0869

Answer #1

The statistical software output for this problem is :

Two sample Z summary hypothesis test:

μ_{1} : Mean of population 1 (Std. dev. = 20)

μ_{2} : Mean of population 2 (Std. dev. = 12)

μ_{1} - μ_{2} : Difference between two means

H_{0} : μ_{1} - μ_{2} = 0

H_{A} : μ_{1} - μ_{2} ≠ 0

**Hypothesis test results:**

Difference | n_{1} |
n_{2} |
Sample mean | Std. err. | Z-stat | P-value |
---|---|---|---|---|---|---|

μ_{1} -
μ_{2} |
250 | 250 | 2 | 1.4751271 | 1.3558154 | 0.1752 |

a. H_{0}: μ_{P} - μ_{C} = 0;
H_{A}: μ_{P} - μ_{C} ≠ 0

standard error (SE) = 1.475127

z score = 1.36

P-value = 0.1738

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