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.

Bertille Justin · Accepted Answer

Final Answer : B, Explanation :  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 = 10population standard deviation (unknown) = cannot calculatez-score for 95% confidence level (two-tailed) = 1.96 (from standard normal distribution table)sample size (unknown) = cannot calculateSince 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 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.

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

Definitions

Learning Objectives

Learning Objectives

Related questions

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.