Question 1Select one answer.10 points

A doctor is measuring the average height of male students at a large college. The doctor measures the heights, in inches, of a sample of 40 male students from the baseball team. Using this data, the doctor calculates the 95% confidence interval (63.5, 74.4).

Which one of the following conclusions is valid?

1. No conclusion can be drawn.
2. The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches.
3. 95% of the male students from the baseball team have heights between 63.5 inches and 74.4 inches.

Question 2Select one answer.10 points

A researcher is estimating the mean income of residents in a large city. The income variable is usually skewed to the right. She collects a random sample of 25 people. The resulting 95% confidence interval is ($26700, $35400).

Which one of the following conclusions is valid?

1. We are 95% confident that the mean income for all residents of this city is between $26700 and $35400.
2. 95% of the residents of this city have an income between $26700 and $35400.
3. No conclusion can be drawn.

Question 3Select one answer.5 points

A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate.

True or false? The researcher could produce a narrower confidence interval by increasing the sample size to 150.

1. True
2. False

Question 4Select one answer.5 points

A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate.

True or false? The researcher could produce a narrower confidence interval by increasing the confidence level to 99%.

1. True
2. False

Question 5Select one answer.5 points

Students in a statistics class conduct a survey to estimate the mean number of units students at their college are enrolled in. The students took a random sample of 50 students from their college. The students calculated a 90% confidence interval to estimate the mean number of units students at their college are enrolled in. The confidence interval was too wide to provide a precise estimate. The students are strategizing about how to produce a narrower confidence interval.

True or false? The students could produce a narrower confidence interval by increasing the confidence level to 95%.

1. True
2. False

Question 6Select one answer.5 points

Students in a statistics class conduct a survey to estimate the mean number of units students at their college are enrolled in. The students took a random sample of 50 students from their college. The students calculated a 90% confidence interval to estimate the mean number of units students at their college are enrolled in. The confidence interval was too wide to provide a precise estimate. The students are strategizing about how to produce a narrower confidence interval.

True or false? The students could produce a narrower confidence interval by increasing the sample size to 100.

1. True
2. False

Question 7Select one answer.10 points

Suppose we take two different random samples from the same population of test scores. The population mean and standard deviation are unknown. The first sample has 25 data values. The second sample has 64 data values. Then we construct a 95% confidence interval for each sample to estimate the population mean.

Which confidence interval will have greater precision (smaller width) for estimating the population mean?

1. The confidence interval based on the sample of 64 data values will be more precise.
2. Both confidence intervals will have the same precision.
3. The confidence interval based on the sample of 25 data values will be more precise.

Question 8Select one answer.10 points

Students in a statistics class take a random sample of 100 students at their college and record how many units each student is enrolled in. The students compute a 90% confidence interval for the mean number of units for students at their college and get (11.93, 12.47).

Next, the students calculate a 95% confidence interval. As the confidence level increases, which of the following will happen to the interval width?

1. Decrease
2. Increase
3. Stay the same