6.1.45 050 A random sample o orty two 200-meter swims has a mean time of 3.032 m
ID: 3040100 • Letter: 6
Question
6.1.45 050 A random sample o orty two 200-meter swims has a mean time of 3.032 minutes and a standard deviation of 0.070 m nutes. A 90%, confidence inter a or te population mean me s son Construct a 90% confidence interval for the population mean time using a standard deviation of 0.04 minutes, which confidence interval is wider? Explain The 90% confidence interval is 3022, 3042 (Round to three decimal places as needed.) Which confidence interval is wider? Explain. Choose the correct answer below. O A. The s-0.070 confidence interval is wider because of the increased variability within the sample. O B. The s 0.04 confidence interval is wider because of the decreased variability within the sample. C. The two intervals are the same size because the confidence interval is based on the level of confidence and sample size.Explanation / Answer
As stated, the 90% confidence interval for s = 0.04 is coming out to be (3.022, 3.042).
Option A is the correct answer.
As the value of the sample standard deviation increases, for the same sample size, the standard error increases and hence the margin of error also increases. This makes the confidence interval wider.
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