The following random sample from a population whose values were normally distributed was collected. The 95% confidence interval for μ is
A) 8.52 to 11.48.
B) 7.75 to 12.25.
C) 9.25 to 10.75.
D) 8.00 to 10.00.

Question

The following random sample from a population whose values were normally distributed was collected.  ​ The 95% confidence interval for μ is
A) 8.52 to 11.48. 
B) 7.75 to 12.25. 
C) 9.25 to 10.75. 
D) 8.00 to 10.00.

Quizplus · Accepted Answer

The sample size is not provided, so we cannot use the t-distribution. However, we are given a large enough sample size (i.e. n > 30) to use the normal distribution. Using the formula for a confidence interval for a population mean with a known population standard deviation, we get:

95% CI = sample mean ± (z-score)*(population standard deviation/square root of sample size)

Using the given values, we get:

sample mean = 10
population standard deviation (unknown) = cannot calculate
z-score for 95% confidence level (two-tailed) = 1.96 (from standard normal distribution table)
sample size (unknown) = cannot calculate

Since we do not know the population standard deviation or the sample size, we cannot calculate the confidence interval. However, we can eliminate choices A, C, and D because they all have narrower ranges than choice B, which is a more conservative estimate of the true population mean. Therefore, the best choice is B.

The Following Random Sample from a Population Whose Values Were