10 SBE11e SM Ch10 1

Chapter 10
Statistical Inference About Means and Proportions with Two Populations

Learning Objectives

1. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population means whenandare known.

2. Know the properties of the sampling distribution of .

3. Be able to use the t distribution to conduct statistical inferences about the difference between two population means whenandare unknown.

4. Learn how to analyze the difference between two population means when the samples are independent and when the samples are matched.

5. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population proportions.

6. Know the properties of the sampling distribution of .

Solutions:

1. a. = 13.6 - 11.6 = 2

b. 1.645

2  .98 (1.02 to 2.98)

c. 1.96

2  1.17 (.83 to 3.17)

2. a.

b. p-value = 1.0000 - .9788 = .0212

c. p-value .05, reject H0. 3. a.

b. p-value = 2(.0630) = .1260

c. p-value > .05, do not reject H0. 4. a. = Population mean for smaller cruise ships

= Population mean for larger cruise ships

= 85.36 – 81.40 = 3.96

b.

c. 3.96 ± 1.88 (2.08 to 5.84)

5. a. = 135.67 – 68.64 = 67.03

b.

c. 67.03  17.08 (49.95 to 84.11) We estimate that men spend $67.03 more than women on Valentine’s Day with a margin of error of $17.08.

6. = Mean hotel price in Atlanta

= Mean hotel price in Houston

H0:

Ha:

p-value = .0351

p-value .05; reject H0. The mean price of a hotel room in Atlanta is lower than the mean price of a hotel room in Houston.

7. a. = Population mean 2002

= Population mean 2003

H0:

Ha:

b. With time in minutes,= 172 - 166 = 6 minutes

c.

p-value = 1.0000 - .9955 = .0045

p-value .05; reject H0. The population mean duration of games in 2003 is less than the population mean in 2002. d.

6  4.5 (1.5 to 10.5)

e. Percentage