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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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