How tall is the average student on your campus? To determine this,you measure the height of a random sample of 200 students,finding a mean height of 166.60 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your fellow students.

Question

Quizplus · Accepted Answer

To construct a confidence interval for the mean height of the students, we can use the formula:

CI = x̄ ± z*(σ/√n)

Where:
CI = Confidence Interval
x̄ = Sample Mean (166.60 cm)
z = Z-Value for the Confidence Interval (From Z-Table, for 90% CI, z=1.645)
σ = Standard Deviation of the Population (5.64 cm)
n = Sample Size (200)

Plugging in the values, we get:

CI = 166.60 ± 1.645*(5.64/√200)
CI = 166.60 ± 0.934
CI = (165.94, 167.26)

Therefore, the best choice is A) (165.94, 167.26) as it gives a 90% confidence interval for the mean height of the students.

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