Question

A hypothetical study concerned with estimating the amount of marijuana use per year among a teenage population obtained a sample of 110 high school students. With the following sample statistics, construct a 95% confidence interval around the mean number of times this sample uses marijuana in a given 6-month period:

X¯ =4.5

s=3.2

A. CI = [3.99, 5.11]

B. CI = [3.89, 5.20]

C. CI = [4.89, 6.33]

D. CI = [3.08, 5.32]

E. CI = [3.89, 5.11]

Part 2.

Using the sample mean and standard deviation in the previous problem, change the sample size to 25 and construct a 95% confidence interval around the mean using the appropriate procedures.

A. CI = [3.11, 5.92]

B. CI = [3.18, 5.82]

C. CI = [3.05, 5.93]

D. CI = [3.33, 5.55]

E. CI = [2.99, 5.88]

Answer 1

Part 1

Given data is

sample size n = 110, so degree of freedom = n-1 = 110-1 = 109

95% confidence level means alpha = 1 - 0.95 = 0.05

by excel function, t critical = T.INV.2T(alpha,df) = T.INV.2T(0.05,109) = 1.982

Confidence interval =

Option E

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Part 2

Given data is

sample size n = 25, so degree of freedom = n-1 = 25-1 = 24

95% confidence level means alpha = 1 - 0.95 = 0.05

by excel function, t critical = T.INV.2T(alpha,df) = T.INV.2T(0.05,24) = 2.064

Confidence interval =

Option B