Use the standard normal distribution or the t-distribution to construct a 95 % c
ID: 3200538 • Letter: U
Question
Use the standard normal distribution or the t-distribution to construct a 95 % confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 45 people, the mean body mass index (BMI) was 26.2 and the standard deviation was 6.17 . Which distribution should be used to construct the confidence interval? Choose the correct answer below.
A. Use a normal distribution because the sample is random, the population is normal, and sigma is known.
B. Use a t-distribution because the sample is random, the population is normal, and sigma is unknown.
C. Use a t-distribution because the sample is random, ngreater than or equals 30, and sigma is unknown.
D. Use a normal distribution because the sample is random, ngreater than or equals 30, and sigma is known.
E. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or nless than 30, and the population is not known to be normal.
Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.
A. The 95 % confidence interval is(____,____). (Round to two decimal places as needed.)
B. Neither distribution can be used to construct the confidence interval. Interpret the results. Choose the correct answer below.
Interpret the resutls. Choose the correct answer below:
With 95 % donfidence, it can be said that the population mean BMI is between the bounds of the confidence interval
It can be said that 95% of people have a BMI between the bounds of the confidence interval.
If a large sample of people are taken approximately 96% of them will have a BMI between the bounds of the confidence interval.
Neither distribution can be used to construct the confidence interval.
Explanation / Answer
The sigma is unknown, n is greater than 30 and population is random and so t distribution must be used. Thus for the first question correct option is C.
t(45-1,0.975)=2.015 t(45-1,0.025)=-2.015
CI is (24.35,28.05)
The interpretation of a confidence interval is that under repeated experiments around 95% of the sample.s will have the sample mean within the interval. So the correct option is "If a large sample of people are taken approximately 95% of them will have a BMI between the bounds of the confidence interval".
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