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.