Question 2 of 5

Question 2

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Elementary Students and Calorie Intake: A public health official is studying differences in nutrition among students at two different elementary schools. They collect a random sample of students independently from each of the two universities and track total calories throughout the day. A score of 1200 or below indicates mild lack of nutrition. A score below 1000 indicates that active treatment is necessary. Sample Statistics

	Size(n)	Mean(x)(x)	SD(s)
Sample 1	60	985	8.7
Sample 2	55	1300	9.6

The official conducts a two-sample t-test to determine whether these data provide significant evidence that students at University 1 are eating less than students at University 2. The test statistic is t = 3.2 with a P-value 0.0009. Which of the following is an appropriate conclusion?

The samples provide significant evidence that students from Sample 1 are eating less than students from Sample 2.

The samples do not provide statistically significant evidence.

We can not use the t-test in this case because the variables (total calories consumed) are likely skewed to the right at each school.

Question 3 of 5

Question 3

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In a study of the impact of eating fruit on birth weight, researchers analyze birth weights (in grams) for babies born to 189 women who gave birth in 2018 at a hospital in California. Suppose in the group, 74 of the women were categorized as "fruit eaters" and 115 as "non-fruit eaters." The difference in the two sample mean birth weights (fruit eaters minus non-fruit eaters) is 21.7 grams and the 95% confidence interval is (-18.5, 18.5)

Which gives the best interpretation of what we can conclude about the impact of eating fruit on birth weight?

This study does not suggest that there is a difference in mean birth weights when we compare fruit eaters to non-fruit eaters.

Eating fruit is associated with higher birth weights. When fruit eaters are compared to non-fruit eaters, we are 95% confident that the mean weight of babies of fruit eaters is between 18.5 grams less to 18.5 grams more than the mean weight of babies of non-fruit eaters.

We are 95% confident that on average, eating fruit causes higher birth weights of between 76.5 grams to 486.9 grams.

There is a 95% chance that if a woman eats fruit during pregnancy her baby will weigh between 76.5 grams to 486.9 grams more than if she did not eat fruit.

Question 4 of 5

Question 4

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Do people see more blame in their partner during times of conflict due to bias? A researcher studying marital problems wants to measure whether couples having problems tend to blame their partners more than themselves. He administered a questionnaire for 50 couples of self blame and one to 50 couples for partner blame.

If ₁and ₂ represent the mean blame scores for each group respectively for partner-blame vs. other-blame, which of the following is the appropriate pair of hypotheses in this case?

H0:12=0Ha:12<0H0:1-2=0Ha:1-2<0

H0:1=2Ha:1<2H0:1=2Ha:1<2

H0:1<2Ha:1=2H0:1<2Ha:1=2

H0:1=2Ha:1>2H0:1=2Ha:1>2

None of the above

Question 5 of 5

Question 5

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Analyses were run. The following is the (edited) output for the test:

Hypothesis Test Results

₁:Test Scores: Partner-blame

₂:Test Scores: Self-blame

Difference	Sample Mean	Std. Err.	DF	T-Stat	P-Value
1 - 2	.11	.67168	94.155815	.163767	0.4351

From the output we learn that:

the data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean score of the partner-blame questionnaire is higher than that of the self-blame questionnaire.

the data provide sufficient evidence reject the H₀; thus, we cannot conclude that the mean score of the partner-blame questionnaire is higher than that of the self-blame questionnaire.

the data do not provide sufficient evidence reject the H₀; thus, we can conclude that the mean score of the partner-blame questionnaire is higher than that of the self-blame questionnaire.

the data provide sufficient evidence to reject H0; thus, we can conclude that the mean score of the partner-blame questionnaire is higher than that of the self-blame questionnaire.