# MATHEMATICS

**Summary statistics are given for independent simple random samples from two populations. Use the**

**pooled t-test to conduct the required hypothesis test.**

12) x1 = 12.5, s1 = 4.1, n1 = 14, x2 = 16.9, s2 = 4.6, n2 = 17

Perform a two-tailed hypothesis test using a significance level of α = 0.05.

**Provide an appropriate response.**

13) In comparing the means of two populations, some methods are based on

independent samples and some are based on paired samples. Explain the

difference between independent and paired samples. Give an example of

each type of sample.

**CHAPTER 10 Answers**

11) -7.92 to -1.28

12) Test statistic: t = -2.782

Critical value = ±2.045

Reject H 0

13) In paired samples, there is a natural pairing of the members of the two populations. In independent

samples, no such pairing exists. An example of an independent sample is the income of men and

women. An example of a paired sample is the income of husbands and their wives. (Examples will

vary.)

**Chapter 12 Final Review**

**Use the chi-square table to find the required **χ**2-value(s).**

14) For a χ2-curve with 23 degrees of freedom, find the χ2-value having

area 0.995 to its right.

15) For a χ2-curve with df = 5, determine χ 2

0.995.

**Perform the required chi-square hypothesis test. Preliminary data analyses and other information**

**indicate that it is reasonable to assume that the variable under consideration is normally distributed.**

**Use the critical-value approach or the P-value approach as indicated.**

16) In 2000, the standard deviation of the scores of all students taking a

particular test was 20.3. In 2005, the standard deviation of the scores of a

random sample of 18 students taking the same test was s = 27.1. At the

5% level of significance, do the data provide sufficient evidence to

conclude that the standard deviation, σ, of all 2005 scores is different

from the 2000 standard deviation of 20.3? Use the P-value approach.

**CHAPTER 12 Answers**

14) 9.260

15) 0.412

16) H0: σ = 20.3 Ha: σ ≠ 20.3

α = 0.05

Test statistic: χ2 = 30.297

0.02 < P < 0.05

Reject the null hypothesis. At the 5% level of significance, the data provide sufficient evidence to

conclude that the standard deviation, σ, of all 2005 scores is different from 20.3.

**Chapter 13 Final Review**

**Find the required F-value.**

17) An F-curve has df = (30, 12). Find the F-value having area 0.01 to its

right.

**Provide an appropriate response.**

18) True or false: In a one-way ANOVA, if the null hypothesis is rejected, we

conclude that the population means are all different (i.e., no two of the

population means are equal).

**Preliminary data analyses indicate that it is reasonable to consider the assumptions for one -way**

**ANOVA satisfied. Perform the required hypothesis test using the critical value approach.**

19) At the 0.025 significance level, do the data provide sufficient evidence to

conclude that a difference exists between the population means of the

four different brands? The sample data are given below. Use One-Way ANOVA.xls. Click Enable Editing and change values to match values in this problem. One-Way ANOVA.xls

**Chapter 13 Answers**

17) 3.70

18) False

19) H0: μ1 = μ = μ3 = μ4. Ha: Not all the means are equal.

Test statistic: F = 0.0555. Critical value: F = 3.95.

Fail to reject the null hypothesis. There is not sufficient evidence to conclude that a difference exists

between the population means of the four different brands.

**Chapter 14 Final Review**

20)The sample data below are the typing speeds (in words per minute) and

reading speeds (in words per minute) of nine randomly selected

secretaries. Here, x denotes typing speed, and y denotes reading

speed.

Use the data to predict the reading speed of a secretary whose typing

speed is 48. In other words, find the regression line, let x = 48 and find the predicted y. Round your answer to the nearest word per minute.

**Provide an appropriate response.**

21) The correlation test for normality involves computing the linear correlation

coefficient between which of the following pairs?

A) The sample data and the population data

B) The predictor variable and the response variable

C) The values of the response variable and their normal scores

D) The sample data and their normal scores

**CHAPTER 14 Answers**

Test statistic: R p = 0.932

Critical value: R *

p = 0.935

Reject H 0 . At the 10% significance level, the data provide sufficient evidence to conclude that

weekly salaries of employees at this company are not normally distributed.

20) 458 words per minute

21) D