A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?" Of 747 subjects, 563 said yes. a. Find a 99% confidence interval for the population proportion who would say yes. O.) (Round to four decimal places as needed.) Can you conclude that the population proportion exceeds 75%? Why? O A. No, we cannot conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval. O B. No, we cannot conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval. Oc. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval. O D. Yes, we can conclude that the population proportion exceeds 75%, because 75% is above the lowest believable value of the confidence interval. b. Without doing any calculations, explain whether the interval in (a) would be wider or narrower than a 95% confidence interval for the population proportion who would say yes. The 99% confidence interval would be narrower than a 95% confidence interval. The 99% confidence interval would be wider than a 95% confidence interval.

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A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?" Of 747 subjects, 563 said yes.
a. Find a 99% confidence interval for the population proportion who would say yes.
| ) (Round to four decimal places as needed.)
Can you conclude that the population proportion exceeds 75%? Why?
O A. No, we cannot conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.
B. No, we cannot conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval.
O C. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.
D. Yes, we can conclude that the population proportion exceeds 75%, because 75% is above the lowest believable value of the confidence interval.
b. Without doing any calculations, explain whether the interval in (a) would be wider or narrower than a 95% confidence interval for the population proportion who would say yes.
O The 99% confidence interval would be narrower than a 95% confidence interval.
The 99% confidence interval would be wider than a 95% confidence interval.
Transcribed Image Text:A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?" Of 747 subjects, 563 said yes. a. Find a 99% confidence interval for the population proportion who would say yes. | ) (Round to four decimal places as needed.) Can you conclude that the population proportion exceeds 75%? Why? O A. No, we cannot conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval. B. No, we cannot conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval. O C. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval. D. Yes, we can conclude that the population proportion exceeds 75%, because 75% is above the lowest believable value of the confidence interval. b. Without doing any calculations, explain whether the interval in (a) would be wider or narrower than a 95% confidence interval for the population proportion who would say yes. O The 99% confidence interval would be narrower than a 95% confidence interval. The 99% confidence interval would be wider than a 95% confidence interval.
Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights,
measured in millimeters, were 55.5, 59.1, 61.3, 63.4, 65.8, and 69.9 9 . Complete parts a through d below.
a. Using technology, find the 95% confidence interval for the population mean u.
(Round to one decimal place as needed.)
b. Name two things you could do to get a narrower interval than the one in part a. Choose the correct choice below.
O A. Decrease the confidence level or increase the sample size.
B. Decrease the confidence level or decrease the sample size.
C. Increase the confidence level or increase the sample size.
D. Increase the confidence level or decrease the sample size.
c. Using technology, construct a 99% confidence interval.
(Round to one decimal place as needed.)
Why is the 99% confidence interval wider than the 95% interval?
O A. The t-distribution critical value is larger with a higher confidence level.
B. The standard deviation is smaller for a higher confidence level.
C. The t-distribution critical value is smaller with a higher confidence level.
D. None of the above statements are correct.
d. On what assumptions is the interval in part a based?
A. The data are obtained by randomization and the population distribution is approximately normal.
B. The data are obtained by randomization and all the data are within two standard deviations of the mean.
C. The data are obtained by randomization and the population distribution is approximately uniform.
D. The population distribution is approximately normal and all the data are within two standard deviations of the mean.
Transcribed Image Text:Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, were 55.5, 59.1, 61.3, 63.4, 65.8, and 69.9 9 . Complete parts a through d below. a. Using technology, find the 95% confidence interval for the population mean u. (Round to one decimal place as needed.) b. Name two things you could do to get a narrower interval than the one in part a. Choose the correct choice below. O A. Decrease the confidence level or increase the sample size. B. Decrease the confidence level or decrease the sample size. C. Increase the confidence level or increase the sample size. D. Increase the confidence level or decrease the sample size. c. Using technology, construct a 99% confidence interval. (Round to one decimal place as needed.) Why is the 99% confidence interval wider than the 95% interval? O A. The t-distribution critical value is larger with a higher confidence level. B. The standard deviation is smaller for a higher confidence level. C. The t-distribution critical value is smaller with a higher confidence level. D. None of the above statements are correct. d. On what assumptions is the interval in part a based? A. The data are obtained by randomization and the population distribution is approximately normal. B. The data are obtained by randomization and all the data are within two standard deviations of the mean. C. The data are obtained by randomization and the population distribution is approximately uniform. D. The population distribution is approximately normal and all the data are within two standard deviations of the mean.
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