110124 (2 complete) This Test: 24 pts possib random sample of forty-seven 200-me

Question

110124 (2 complete) This Test: 24 pts possib random sample of forty-seven 200-meter swims has a mean time of 3.051 minutes. The population standard deviation is 0 070 minutes. A 90% confidence interval or the population mean time is (3.034,3.068) Construct a 90% confidence interval for the population mean ti The 90% confidence interval is OD e using a population standard deviation of 0 04 minutes which conii ce ite als id r? Explain Round to three decimal places as needed.) Which confidence interval is wider? Explain. Choose the correct answer below A. The : 0 04 confidence interval is wider because of the decreased variability within the sample O B. The :0 070 confidence interval is wider because of the increased variability within the sample O C. The two interva als are the same size because the confidence interval is based on the level of confidence and sample sice Click to select your answer(s) Type here to search

Explanation / Answer

Solution:

Sample Mean x = 3.051
Population Standard deviation = 0.070
Sample size n = 47
Singnificance level = 0.10
Z/2 = Z0.05 = 1.645
Confidence interval = x ± Z/2 * (/n)
= 3.051 ± 1.645 * (0.070/sqrt(47))
= (3.034, 3.068)
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Sample Mean x = 3.051
Population Standard deviation = 0.04
Sample size n = 47
Singnificance level = 0.10
Z/2 = Z0.05 = 1.645
Confidence interval = x ± Z/2 * (/n)
= 3.051 ± 1.645 * (0.04/sqrt(47))
= (3.041, 3.061)
B. The = 0.070 confidence interval is wider because of the increased variability within the sample

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