Question

4 a family tracked the number of pounds of turkey they consumed each thanksgiving for the past 10 years. the data are shown below: pounds of turkey: 12, 18, 14, 18, 16, 20, 18, 17, 19, 18. mean: 16.4 sd: 2.46 the family realized later that their scale was measuring turkeys as 2 pounds heavier than the true weight and they adjusted each number in the list to account for this error. what is the new mean and standard deviation of the data? 5. a group of researchers wants to investigate whether eating pumpkin pie on thanksgiving day leads to increased feelings of happiness. they recruit 100 volunteers and randomly assign them to one of two groups: - group a: eat a slice of pumpkin pie as part of thanksgiving dinner. - group b: do not eat any pumpkin pie as part of thanksgiving dinner. one hour after dinner, the researchers ask the participants to rate their happiness on a scale of 1 to 10. they found that participants who ate pumpkin pie reported significantly higher levels of happiness. which of the following is the most appropriate conclusion?

Explanation:

Question 4

Step1: Analyze effect on mean

The original mean is \( 18.4 \). Each data point is decreased by \( 4 \) (since the scale measured \( 4 \) pounds heavier). The mean of a set of data is the sum of the data points divided by the number of data points. If each data point is decreased by \( 4 \), the new mean \( \mu_{new} \) is \( \mu_{old}- 4 \). So \( 18.4 - 4=14.4 \).

Step2: Analyze effect on standard deviation

The standard deviation measures the spread of the data. If we subtract a constant from each data point, the spread (distance between data points) remains the same. So the standard deviation will not change. The original standard deviation is \( 2.46 \), so the new standard deviation is also \( 2.46 \).

This is a randomized controlled experiment (random assignment to groups). In such experiments, if we find a significant difference between the groups, we can infer causality for the population from which the sample (volunteers here) is drawn. The researchers randomly assigned 100 volunteers to two groups (ate pumpkin pie or not) and found a significant difference in happiness. So we can conclude that eating pumpkin pie (as per this study's setup) causes increased happiness for people like the volunteers. Option B is wrong because 100 is a reasonable sample size. Option C is wrong as the study found a relationship. Option D is wrong because in a randomized experiment, we can infer causality. Option E is wrong because using volunteers is a common sampling method and doesn't prevent drawing conclusions if the experiment is well - designed (random assignment is done).

Answer:

B. Mean: 14.4, Standard Deviation: 2.46

Question 5