Question 1

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 2

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 3

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 4

If a 95% confidence interval for the mean was computed as (25,50), then if several more samples were taken with the same sample size, then 95% of them would have a sample mean between 25 and 50.

• True
• False

Question 5

If n = 16,xx= 34, and s = 15, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places. <<

Question 6

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 78.4 for a sample of size 22 and standard deviation 10.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).Assume the data is from a normally distributed population.

Enter your answer as a tri-linear inequality accurate to three decimal places. <<

Question 7

A researcher is interested in finding a 90% confidence interval for the mean number of times per day that college students text. The study included 107 students who averaged 31.2 texts per day. The standard deviation was 19.5 texts.

a. To compute the confidence interval use a ? t z distribution.

b. With90% confidence the population mean number of texts per day is between and texts.

c.If many groups of 107 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day.

Question 8

A researcher is interested in finding a 98% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 150 students who averaged 39.4 minutes concentrating on their professor during the hour lecture. The standard deviation was 13.4 minutes.Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z t distribution.

b. With98% confidence the population mean minutes of concentration is between and minutes.

c.If many groups of 150 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration.

Question 9

You are interested in finding a 98% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 15 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.

15

20

9

13

21

5

18

7

8

24

10

17

28

15

7

a. To compute the confidence interval use a ? t z distribution.

b. With98% confidence the population mean number of visits per physical therapy patient is between and visits.

c.If many groups of 15 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per patient and about percent will not contain the true population mean number of visits per patient.

Question 10

You are interested in finding a 95% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students.

21

7

7

17

23

16

25

5

24

17

6

14

a. To compute the confidence interval use a ? t z distribution.

b. With95% confidence the population mean commute for non-residential college students is between and miles.

c.If many groups of 12 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of commute miles and about percent will not contain the true population mean number of commute miles.

Question 11

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately=35.6=35.6. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required? n=

Question 12

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately=27.4=27.4. You would like to be 99% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?Do not round mid-calculation. n=

Question 13

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 14

Express the confidence interval23.3%5.6%23.3%5.6%in the form of a trilinear inequality. %

Question 15

If n = 110 and X = 88, construct a 95% confidence interval for the population proportion, p. Give your answers to three decimals < p <

Question 16

Out of 400 people sampled, 56 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to four places < p <

Question 17

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 389 randomly selected caterpillars observed, 53 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between and .

b. If many groups of 389 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

Question 18

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximatelyp*=81%p*=81%. You would like to be 99% confident that you estimate is within 1.5% of the true population proportion. How large of a sample size is required?

n=

Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Question 19

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 98% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required? n= Do not round mid-calculation. However, use of a critical value rounded to three decimal places will suffice.