Question

Prominent candy company Sweetums and fast food chain Paunch Burger decide to team up and release a new child-sized drink that blends candy bars into milkshakes. Leslie Knope is interested in how this new milkshake affects the weight of the citizens of her town (Pawnee, Indiana). She decides to take a random sample of 41 people from the town and asks the people in the sample to replace one beverage a day with this new candy bar milkshake. She measures their weights (in kilograms) before and after drinking this milkshake for a week. The summary of the data is below.

Variable Sample Mean Sample Standard Deviation

Weight (After - Before) 3.51 7.44

Use a significance level of α = 0.01 to test the hypothesis that the mean weight of citizens in Pawnee significantly increased after drinking the new child-sized candy bar milkshake from Sweetums and Paunch Burger for a week. Assume that the necessary conditions hold to carry out this test.

Select one:

t = 2.293, p-value < 0.01, reject the null hypothesis, and conclude that the mean weight of the citizens has increased.

t = 2.293, p-value < 0.01, reject the null hypothesis, and conclude that the mean weight of the citizens has changed.

t = 3.021, p-value > 0.01, do not reject the null hypothesis, conclude that the mean weight of the citizens has stayed the same.

t = 2.293, p-value > 0.01, do not reject the null hypothesis, conclude that the mean weight of the citizens has stayed the same.

t = 3.021, p-value < 0.01, reject the null hypothesis, and conclude that the mean weight of the citizens has increased.

To estimate the effect of the new child-sized candy bar milkshake, Leslie finds a 95% confidence interval for the mean difference in weight to be (1.163 , 5.857).

Answer 1

Given:

n = 41, sample mean () = 3.51, sample standard deviation (Sd) = 7.44

Calculation:

Test statistic:

Degree of freedom = n-1 = 41-1 = 40

P-value: 0.0022 ........................Using t table

Conclusion:

P-value < , i.e. 0.0022 < 0.01, that is Reject Ho at 1% level of signiifcance.

ANSWER: E.

t = 3.021, p-value < 0.01, reject the null hypothesis, and conclude that the mean weight of the citizens has increased.