High School

A simple random sample of 20 items resulted in a sample mean of 60. The population standard deviation is [tex]\sigma = 15[/tex].

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.

A) Lower limit: 56.3; Upper limit: 63.7
B) Lower limit: 58.5; Upper limit: 61.5
C) Lower limit: 53.5; Upper limit: 66.5
D) Lower limit: 59.1; Upper limit: 60.9

Answer :

Final answer:

The 95% confidence interval for the population mean is (56.3, 63.7).

Explanation:

To compute the 95% confidence interval for the population mean, we can use the formula:

Lower limit = sample mean - (critical value * standard deviation / square root of sample size)

Upper limit = sample mean + (critical value * standard deviation / square root of sample size)

Plugging in the given values, we have:

Lower limit = 60 - (1.96 * 15 / sqrt(20)) ≈ 56.3

Upper limit = 60 + (1.96 * 15 / sqrt(20)) ≈ 63.7

Therefore, the 95% confidence interval for the population mean is (56.3, 63.7).

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