Question 1

A sample of size 42 college students produced a 95% confidence interval of (3.1, 5.2) for the mean number of coats owned. Then there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.

• True
• False

Question 2

Suppose a researcher collected data with n = 200 and came up with a sample mean of 83 and 95% confidence interval (78, 88). If the researcher collected another sample from the same population with n = 200, there would be a 95% chance that the researcher would come up with a confidence interval of (78,88) for this new data set.

• True
• False

Question 3

A 95% confidence interval for the mean number of miles that college students live from campus was computed to be [0.9, 2.3]. Then a randomly selected college student will have a 95% chance of living between 0.9 and 2.3 miles from campus.

• True
• False

Question 4

If 50 students are surveyed about how many units they are taking and a 95% confidence interval is computed to be [14,18], then with 95% confidence we can state that the mean of these students' unit load is between 14 and 18.

• True
• False

Question 5

A survey was done of 55 Lake Tahoe residents to see how many times they went to a Lake Tahoe beach last summer. The 95% confidence interval for the mean was found to be (3.1,7.2). Then we can be 95% confident that these 55 Tahoe residents went to the beach on average between 3.1 and 7.2 times last summer.

• True
• False

Question 6

If a 95% confidence interval for the mean number of hours that students study per week is (18,23), then there is a 95% chance that a randomly selected student will study between 18 to 23 hours per week.

• True
• False

Question 7

If we survey 35 American citizens asking them if they were born in a foreign country, then it is appropriate to use the normal distribution when calculating the confidence interval for the proportion of American citizens who were born in a foreign country since the sample size is greater than 30.

• True
• False

Question 8

With a large sample size such as n = 100, we do not need to assume the distribution is normal in order to compute a 95% confidence interval for the mean.

• True
• False

Question 9

A 95% confidence interval for the mean was computed with a sample of size 90 to be (16,22). Then the Error 3.

• True
• False

Question 10

Suppose data was collected with n = 36 to compute a 95% confidence interval. If the population standard deviation is 2400, then the Error is 784.

• True
• False

Question 11

If we have already decided on the Error and confidence level for a confidence interval, then a population with a standard deviation of 30 will require a greater sample size than a population with a standard deviation of 20.

• True
• False

Question 12

If the sample mean and sample standard deviation are found to be 90 and 15 respectively and the sample size is 35, then it is better to use the Z distribution than the T distribution for the calculations, since the sample size is greater than 30.

• True
• False

Question 13

A researcher computed a 90% confidence interval for the proportion of students who smoke. If the researcher had instead used a 95% confidence interval, then the computed margin of error would have been smaller.

• True
• False

Question 14

If the confidence level is decreased and the standard deviation and sample size stay the same, then the Error will be increased.

• True
• False

Question 15

If the standard deviation is increased and the sample size and the confidence level stay the same, then the Error will also be increased.

• True
• False

Question 16

If the standard deviation is increased and the sample size and confidence level stay the same, then the margin of error will also be increased.

• True
• False

Question 17

If we have already decided on the Error and confidence level for a confidence interval, then a population with a standard deviation of 30 will require a greater sample size than a population with a standard deviation of 20.

• True
• False

Question 18

If the sample size is increased and the standard deviation and confidence level stay the same, then the margin of error will also be increased.

• True
• False