A researcher surveyed 100 elderly people. For each person the researcher conducted a questionnaire that measures their level of happiness (on a scale from 1 to 20). The researcher also asked each person how many medications they take per week. The correlation coefficient between these two variables was calculated to be -0.67. According to this information ....

Question

Question 16 options:

This is an observational study, so although the two variables appear to have an association, we cannot conclude that either variable is causing a change in the other variable.

We can conclude that the number of medications an elderly person has to take negatively impacts their level of happiness.

We can conclude that an elderly person's level of happiness has a negative impact on the number of medications they have to take weekly.

We can conclude that if we want elderly people to have more happiness in their lives, they should take more weekly medications.

Question 17 (1 point)

Using a sample of Boston Marathon winning times and the year the race was run, a regression equation of y = -0.3X + 732.3 was calculated where the winning time can be predicted (response variable) using the year the race was run (explanatory variable). The correlation coefficient was calculated to be -0.79. Which of the following is an explanation of the meaning of the slope?

Question 17 options:

For every year that passes, we expect the average winning time to decrease by 0.3 minutes.

For every year that passes, we expect the average winning time to increase by 0.3 minutes.

For every year that passes, we expect the average winning time to decrease by 0.79 minutes.

For every year that passes, we expect the average winning time to increase by 0.79 minutes.

Question 18 (1 point)

Thirty students were randomly sampled to determine the number of classes students take per semester. The sample mean was calculated to be 4.11 classes. A 90% confidence interval for the data was calculated to be 3.89 to 4.33. Find the value of the margin of error (MOE) for a 90% confidence interval.

Question 18 options:

0.44

0.33

0.22

0.11

Question 19 (1 point)

Suppose I've taken a sample, calculated a sample statistic, and constructed a 95% confidence interval. If I were to use the same data but change the confidence level to 99%, what would happen to the interval?

Question 19 options:

It would become narrower.

It would not change.

It would become wider.

Not enough information provided to determine

Question 20 (1 point)

A 95% confidence interval on the population mean amount of water used per household during the month of May in a city wa calculated to be 9422 gallons to 9930 gallons. Which of the following is an appropriate explanation of this interval?

Question 20 options:

We are 95% sure that all households use between 9422 gallons and 9930 gallons of water during the month of May in this city.

We know there is a 95% chance a household will use between 9422 gallons and 9930 gallons of water during the month of May in this city.

We are sure 95% of households in this city used between 9422 gallons and 9930 gallons of water during the month of May.

We are 95% sure the mean amount of water used per households in this city was between 9422 gallons and 9930 gallons during the month of May.

Answer 1

Let's go through each question one by one:

Question 16: This is an observational study, so although the two variables appear to have an association, we cannot conclude that either variable is causing a change in the other variable.

Correct answer: This is an observational study, so although the two variables appear to have an association, we cannot conclude that either variable is causing a change in the other variable.

Question 17: The slope of a regression equation represents the change in the response variable for a one-unit increase in the explanatory variable. Thus, a slope of -0.3 indicates that for every year that passes, the average winning time (in minutes) is expected to decrease by 0.3 minutes.

Correct answer: For every year that passes, we expect the average winning time to decrease by 0.3 minutes.

Question 18: The margin of error (MOE) is calculated as half the width of the confidence interval. The interval ranges from 3.89 to 4.33, so the width is 4.33 - 3.89 = 0.44. Thus, the MOE is 0.44 / 2 = 0.22.

Correct answer: 0.22

Question 19: When increasing the confidence level from 95% to 99%, the confidence interval will become wider because a higher confidence level requires a broader range to ensure that the true parameter is captured within the interval.

Correct answer: It would become wider.

Question 20: A 95% confidence interval indicates that we are confident that the true population mean is within that range, but it does not imply that all households or any individual household will use that amount of water. Therefore, the correct interpretation is regarding the mean.

Correct answer: We are 95% sure the mean amount of water used per households in this city was between 9422 gallons and 9930 gallons during the month of May.

Summary of answers:

• Q16: First option
• Q17: First option
• Q18: Third option (0.22)
• Q19: Third option (It would become wider.)
• Q20: Fourth option (We are 95% sure the mean amount...)