Q1 -

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

		Population
		1	2
Sample Size		39	46
Sample Mean		9.4	7.3
Sample Variance		8.52	14.52

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?

- 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}.

- 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}.

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

Q4 -

Independent random samples were selected from two quantitative populations, with sample sizes, means, and standard deviations given below.

n₁ = n₂ = 90,

x₁ = 125.1,

x₂ = 123.6,

s₁ = 5.7,

s₂ = 6.5

Construct a 95% confidence interval for the difference in the population means (_{1 2}). (Round your answers to two decimal places.)

??? to ???

Find a point estimate for the difference in the population means.

???

Calculate the margin of error. (Round your answer to two decimal places.)

???

Compare your results. Can you conclude that there is a difference in the two population means (_{1 2})?

The confidence interval and the point estimate together with the margin of error suggest (different conclusions / the same conclusion)---??Select??---. Since the value _{1 2} = 0 is ( in / not in)---??Select??--- the interval, the confidence interval suggests it is (possible the two population means are the same / likely the two population means are the different)---??Select??---. The range of values given by the point estimate the margin of error ( does not include / includes) ---??Select??--- does not include includes 0. This suggests that the two population means are (probably different / possibly the same) ---??Select??--- probably different possibly the same .

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

Q5 -

For the given confidence interval, can you conclude that there is a difference between ₁ and ₂?

Explain.

137.3 < _{1 2} < 138.5

Since the value _{1 2} = 0 (is / not is) ---??Select??--- in the confidence interval, it is (unlikely / plausible)---??Select??--- that _{1 2} = 0. You (cannot / can)---??Select??--- conclude that there is a difference in the two population means.

Q6-

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		2.4	3.1
Sample Variance		1.84	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 shift.

Interpret the interval.

- 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.

- 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.

- 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.

Q7 -

As a group, students majoring in engineering disciplines have the highest salary expectations, followed by those studying the computer science fields, according to the results of a study. To compare the starting salaries of college graduates majoring in electrical engineering and computer science, random samples of 60 recent college graduates in each major were selected and the following information obtained.

Major	Mean ($)	SD
Electrical Engineering	62,232	12,900
Computer science	57,565	13,930

(a)Find a point estimate for the difference in the average starting salaries (in dollars) of college students majoring in electrical engineering and computer science. (Use electrical engineering computer science.)

$ ???

What is the 95% margin of error (in dollars) for your estimate? (Round your answer to two decimal places.)

$???

(b)Based upon the results in part (a), do you think that there is a significant difference in the average starting salaries for electrical engineers and computer scientists? Explain.

Since the margin of error of the estimate of the difference _{1 2} allows (only positive / only negative / both positive and negative) ---??Select??--estimates, the mean expected salary for electrical engineering majors (is likely greater than / cannot be said to be different from / is likely less than)---??Select??--- the mean for computer science majors.

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

Q8 -

Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for the data are given in the table.

	Hotel A	Hotel B	Hotel C
Sample Average ($)	135	180	120
Sample Standard Deviation	17.6	22.9	12.5

(a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Use Hotel A Hotel B. Round your answers to two decimal places.)

$ ?? to $ ??

(b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Use Hotel B Hotel C. Round your answers to two decimal places.)

$ ?? to $ ??

(c) Do the intervals in parts (a) and (b) contain the value

(_{1 2}) = 0?

- Yes, the interval in part (a) contains (_{1 2}) = 0.

- Yes, the interval in part (b) contains (_{1 2}) = 0.

- Yes, both intervals contain (_{1 2}) = 0.

- No, neither interval contains (_{1 2}) = 0.

Why is this of interest to the researcher?

- If (_{1 2}) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.

- If (_{1 2}) = 0 is contained in the confidence interval, it is implied that we cannot conclude there is a difference in the average room rates for the two hotels.

- If (_{1 2}) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0.

- If (_{1 2}) = 0 is contained in the confidence interval, it is implied that there was an error in the database records.

- If (_{1 2}) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.

(d) Do the data indicate a difference in the average room rates between the Hotel A and the Hotel B chains?

- Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel B chains.

- No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel B chains.

Do the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains?

- Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains.

- No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains.

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