Question

A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 19 students, the mean age is found to be 22.4 years. From past studies, the ages of enrolled students are normally distributed with a standard deviation of 9.5 years. Construct a 90% confidence interval for the mean age of all students currently enrolled.

1. what is the critical value ?

2. the margin of error?

Answer 1

Formula for Confidence Interval for population Mean When Population Standard deviation is known

Critical value : Z/2

Margin of error :

1.

for 90% confidence level = (100-90)/100 =0.10

/2 = 0.10/2 =0.05

Z/2 = Z0.05 = 1.6449

Critical value =  Z/2 = Z0.05 = 1.6449

Critical value = 1.6449

2.

Given,

sample size : n: Number od students in the random sample = 19

Population standard devaition : the ages of enrolled students are normally distributed with a standard deviation = 9.5 years

Margin of error :

Margin of error = 3.383

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90% confidence interval for the mean age of all students currently enrolled