1 - Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below.

		Population
		1	2
Sample Size		39	43
Sample Mean		9.5	7.3
Sample Variance		8.7	14.32

Construct a 90% confidence interval for the difference in the population means. (Use _{1 2}. Round your answers to two decimal places.)

???? to ????

Construct a 99% confidence interval for the difference in the population means. (Round your answers to two decimal places.)

???? to ????

What does the phrase "90% confident" or "99% confident" mean?

In repeated sampling, 10% (or 1% as the case may be) of all intervals constructed in this manner will enclose _{1 2}. Hence, we are fairly certain that this particular interval contains _{1 2}.

There is a 90% (or 99% as the case may be) probability that the interval will enclose _{1 2}. Hence, we are fairly certain that this particular interval contains _{1 2}.

In repeated sampling, 90% (or 99% as the case may be) of all intervals constructed in this manner will enclose _{1 2}. Hence, we are fairly certain that this particular interval contains _{1 2}.

90% (or 99% as the case may be) of all values from populations 1 and 2 will fall within the interval. Hence, we are fairly certain that this particular interval contains _{1 2}.

There is a 90% (or 99% as the case may be) chance that for any two samples, one sample from population 1 and one sample from population 2, the difference between sample means will fall within the interval. Hence, we are fairly certain that this particular interval contains _{1 2}.

2 - Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below.

		Population
		1	2
Sample Size		48	54
Sample Mean		10.4	8.2
Sample Variance		9.53	15.42

A 90% confidence interval for _{1 2} is 1.06 to 3.34 and a 99% confidence interval for _{1 2} is 0.41 to 3.99. Use these confidence intervals to answer the questions.

Can you conclude with 99% confidence that there is a difference in the means for the two populations?

Yes. The value _{1 2} = 0 is in the interval which suggests that there is likely a difference between ₁ and ₂.

No. The value _{1 2} = 0 is in the interval which does not suggest that there is a difference between ₁ and ₂.

No. The value _{1 2} = 0 is not in the interval which does not suggest that there is a difference between ₁ and ₂.

Yes. The value _{1 2} = 0 is not in the interval which suggests that there is likely a difference between ₁ and ₂.

Can you conclude with 99% confidence that there is a difference in the means for the two populations?

Yes. The value _{1 2} = 0 is in the interval which suggests that there is likely a difference between ₁ and ₂.

No. The value _{1 2} = 0 is in the interval which does not suggest that there is a difference between ₁ and ₂.

No. The value _{1 2} = 0 is not in the interval which does not suggest that there is a difference between ₁ and ₂.

Yes. The value _{1 2} = 0 is not in the interval which suggests that there is likely a difference between ₁ and ₂.

3 - Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below.

		Population
		1	2
Sample Size		49	49
Sample Mean		5.3	6.7
Sample Variance		9.55	10.32

A 90% confidence interval for _{1 2} is 2.45 to 0.35 and a 99% confidence interval for _{1 2} is 3.04 ton 0.24. Use these confidence intervals to answer the questions.

Can you conclude with 90% confidence that there is a difference in the means for the two populations?

No. The value _{1 2} = 0 is in the interval which does not suggest that there is a difference between ₁ and ₂.

No. The value _{1 2} = 0 is not in the interval which does not suggest that there is a difference between ₁ and ₂.

Yes. The value _{1 2} = 0 is in the interval which suggests that there is likely a difference between ₁ and ₂.

Yes. The value _{1 2} = 0 is not in the interval which suggests that there is likely a difference between ₁ and ₂.

Can you conclude with 99% confidence that there is a difference in the means for the two populations?

No. The value _{1 2} = 0 is in the interval which does not suggest that there is a difference between ₁ and ₂.

No. The value _{1 2} = 0 is not in the interval which does not suggest that there is a difference between ₁ and ₂.

Yes. The value _{1 2} = 0 is in the interval which suggests that there is likely a difference between ₁ and ₂.

Yes. The value _{1 2} = 0 is not in the interval which suggests that there is likely a difference between ₁ and ₂.

6 - Samples of 100 8-hour shifts were randomly selected from the police records for each of two districts in a large city. The number of police emergency calls was recorded for each shift. The sample statistics are listed below.

		Region
		1	2
Sample Size		100	100
Sample Mean		2.5	3.3
Sample Variance		1.54	2.74

Find a 90% confidence interval for the difference in the mean numbers of police emergency calls per shift between the two districts of the city. (Use _{1 2}. Round your answers to two decimal places.)

??? calls per shift to ???? calls per shiftInterpret the interval.

In repeated sampling, 90% of all intervals constructed in this manner will enclose the difference in the population mean number of police emergency calls per 8-hour shift between region 1 and region 2. Hence, we are fairly certain that this particular interval contains a difference in the population means from region 1 and region 2.

In repeated sampling, 10% of all intervals constructed in this manner will enclose the difference in the population mean number of police emergency calls per 8-hour shift between region 1 and region 2. Hence, we are fairly certain that this particular interval contains a difference in the population means from region 1 and region 2.

There is a 90% chance that for any two samples, one sample from region 1 and one sample from region 1, the difference between sample mean number of police emergency calls per 8-hour shift will fall within the interval. Hence, we are fairly certain that this particular interval contains a difference in the sample means from region 1 and region 2.

90% of all values from the populations in region 1 and region 2 will fall within the interval. Hence, we are fairly certain that this particular interval contains a difference in the sample means from region 1 and region 2.

You may need to use the appropriate appendix table or technology to answer this question.