Question

A random sample of fifty dash eight ​200-meter swims has a mean time of 3.253 minutes. The population standard deviation is 0.060 minutes. A 95​% confidence interval for the population mean time is left parenthesis 3.240 comma 3.266 right parenthesis.

Construct a

9595​%

confidence interval for the population mean time using a population standard deviation of

0.030.03

minutes. Which confidence interval is​ wider? Explain.

The

9595​%

confidence interval is

​(nothing​,nothing​).

​(Round to three decimal places as​ needed.)

Which confidence interval is​ wider? Explain. Choose the correct answer below.

A.The

sigmaσequals=0.030.03

confidence interval is wider because of the decreased variability within the sample.

B.The

sigmaσequals=0.0600.060

confidence interval is wider because of the increased 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.

Answer 1

using TI 84 calculator

press stat then tests then Zinterval

enter the data set

xbar = 3.253

sigma = 0.03

n = 58

c-level = 0.95

press enter, we get

confidence interval = (3.245, 3.261)

Correct answer is option B

The σ =0.060 confidence interval is wider because of the increased variability within the sample.

we know that confidence interval width is directly proportional to the standard deviation. So, a larger standard deviation will give us wider confidence interval as compared to smaller standard deviation.