Question

Suppose that a sample of size 10 is selected from a population with unknown variance. If this information is used to construct a confidence interval for a single population mean, which of the following statements is true?

Select the best answer.

The sample of size 10 must be normally distributed.

The standard normal distribution must be used to construct the confidence interval.

The sample mean cannot be used as a point estimate for the population mean because the sample size is small.

The population from which the sample was obtained is assumed to be normally distributed.

A researcher is analyzing demographic characteristics of two television programs (program 1 and program 2). The characteristic of interest was the average ages of the two audiences. The researcher randomly selected 15 people from each audience, and reported the following: the average age of the audience for program 1 = 43 years, the average age of the audience for program 2 = 45 years, the sample standard deviation for the ages of the audience for program 1 = 5, and the sample standard deviation for the ages of the audience for program 2 = 8. A 98% confidence interval for the difference in the mean age (audience for program 2 - audience for program 1) is

Select the best answer.

-4.0096 years to 8.0096 years

3.5693 years to 7.5693 years

2.1437 years to 6.1437 years

2.9896 years to 6.9896 years

Answer 1

Suppose that a sample of size 10 is selected from a population with unknown variance. If this information is used to construct a confidence interval for a single population mean, which of the following statements is true?

Select the best answer.

Ans:

The population from which the sample was obtained is assumed to be normally distributed.

2). The characteristic of interest was the average ages of the two audiences. The researcher randomly selected 15 people from each audience, and reported the following: the average age of the audience for program 1 = 43 years, the average age of the audience for program 2 = 45 years, the sample standard deviation for the ages of the audience for program 1 = 5, and the sample standard deviation for the ages of the audience for program 2 = 8. A 98% confidence interval for the difference in the mean age (audience for program 2 - audience for program 1) is

Formula for Confidence Interval for Difference in two Population means

n₁ = n₂ = 15

= 43 ; = 45

s₁ = 5

s₂ = 8

Degrees of freedom = n₁ + n₂ -2 = 15+15-2=28

for 98% confidence level =(100-98)/100 =0.02

/2 =0.02/2=0.01

98% confidence interval for the difference in the mean age (audience for program 2 - audience for program 1) is

Select the best answer.

Ans : -4.0096 years to 8.0096 years