solution:
sample size =n= 40
sample mean = = 26.9
sample standard deviation = S = 6.03
As the sample is randomly selected and standard deviation of the population is unknown so we use the t-distribution.
correct answer
B ) using a t distribution because the sample is random , the population is normal and the is unknown
step 2
significance level == 1 - 0.99 = 0.01
degree of freedom = df = n - 1 = 40-1 = 39
critical value of t by using the t table =
margin of error(E) =
confidance interval =
lower bound of interval = 26.9 - 2.58 = 24.32
upper bound of interval = 26.9 + 2.58 = 29.48
correct choice is A) The 99% confidence interval is (24.32, 29.48)
part c)
interpretation of confidance interval
B) with 99% confidance , it can be said that the population mean BMI is between the bounds of confidence interval.
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