ALEKS 360 ELEM STATISTICS
ALEKS 360 ELEM STATISTICS
10th Edition
ISBN: 9781264241385
Author: Bluman
Publisher: MCG
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Textbook Question
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Chapter 9, Problem 9.2.5RE

For each exercise, perform these steps. Assume that all variables are normally or approximately normally distributed.

a. State the hypotheses and identify the claim.

b. Find the critical value(s).

c. Compute the test value.

d. Make the decision.

e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified.

5. Teachers’ Salaries A random sample of 15 teachers from Rhode Island has an average salary of $35,270, with a standard deviation of $3256. A random sample of 30 teachers from New York has an average salary of $29,512, with a standard deviation of $1432. Is there a significant difference in teachers’ salaries between the two states? Use α = 0.02. Find the 98% confidence interval for the difference of the two means.

a.

Expert Solution
Check Mark
To determine

To identify: The claim and state H0 and Ha .

Answer to Problem 9.2.5RE

The claim is that “there is a significant difference in teachers’ salaries between the two states”.

The hypotheses are given below:

Null hypothesis: H0:μ1=μ2

Alternative hypothesis: H1:μ1μ2 (claim)

Explanation of Solution

Given info:

x¯1=$35,270 , x¯2=10.3 , s1=$3,256 , s2=$1,432 , n1=15 , and n2=30 .

Justification:

Here, there is a significant difference in teachers’ salaries between the two states is tested. Hence, the claim is that there is a significant difference in teachers’ salaries between the two states. This can be written as μ1μ2 . The complement of the claim is μ1=μ2 . In the given experiment, the alternative hypothesis indicates the claim.

The hypotheses are given below:

Null hypothesis:

H0:μ1=μ2

Alternative hypothesis:

H1:μ1μ2

b.

Expert Solution
Check Mark
To determine

To find: The critical value α=0.02 .

Answer to Problem 9.2.5RE

The critical value at α=0.02 is ±2.624 .

Explanation of Solution

Calculation:

Here, the test is two tailed test.

Critical value:

Here, variances are not equal. Hence, the degrees of freedom is,

df=Smallar of n11 and  n21=151=14

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘t’ distribution.
  • In Degrees of freedom, enter 14.
  • Click the Shaded Area tab.
  • Choose Probability value and Two Tail for the region of the curve to shade.
  • Enter the Probability value as 0.02.
  • Click OK.

Output using the MINITAB software is given below:

ALEKS 360 ELEM STATISTICS, Chapter 9, Problem 9.2.5RE , additional homework tip  1

From the output, the critical value is ±2.624 .

c.

Expert Solution
Check Mark
To determine

To find: The test value.

To find: The 98% confidence interval for the difference of the two means.

Answer to Problem 9.2.5RE

The test value is –0.9.

The 98% confidence interval for the difference of the two means is 3,483<μ1μ2<8,033_ .

Explanation of Solution

Calculation:

Test statistic:

Software Procedure:

Step by step procedure to obtain test statistic using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Sample t.
  • Choose Summarized data.
  • In first, enter Sample size as15, Mean as 35,270, Standard deviation as 3,256.
  • In second, enter Sample size as30, Mean as 29,512, Standard deviation as 1,432.
  • Choose Options.
  • In Confidence level, enter 98.
  • In Alternative, select not equal.
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

ALEKS 360 ELEM STATISTICS, Chapter 9, Problem 9.2.5RE , additional homework tip  2

From the MINITAB output, the test value is 6.54 and the 98% confidence interval for the difference of the two means is 3,483<μ1μ2<8,033_ .

d.

Expert Solution
Check Mark
To determine

To make: The decision.

Answer to Problem 9.2.5RE

The decision is that, the null hypothesis isrejected.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to indicate the appropriate area and critical value using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘t’ distribution.
  • In Degrees of freedom, enter 8.
  • Click the Shaded Area tab.
  • Choose Probability value and Two Tail for the region of the curve to shade.
  • Enter the Probability value as 0.02.
  • Enter 6.54 under show reference lines at X values
  • Click OK.

Output using the MINITAB software is given below:

ALEKS 360 ELEM STATISTICS, Chapter 9, Problem 9.2.5RE , additional homework tip  3

From the output, it can be observed that the test statistic value falls in the critical region. Therefore, the null hypothesis isrejected.

e.

Expert Solution
Check Mark
To determine

To summarize: The result.

Answer to Problem 9.2.5RE

The conclusion is that, there is enough evidence to support the claim that there is a significant difference in teachers’ salaries between the two states.

Explanation of Solution

Justification:

From part (d), the null hypothesis is rejected. Thus, there is enough evidence to support the claim that there is a significant difference in teachers’ salaries between the two states.

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Chapter 9 Solutions

ALEKS 360 ELEM STATISTICS

Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - Prob. 13ECh. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - Self-Esteem Scores In a study of a group of women...Ch. 9.1 - Ages of College Students The dean of students...Ch. 9.1 - Working Breath Rate Two random samples of 32...Ch. 9.1 - Traveling Distances Find the 95% confidence...Ch. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Television Watching The average number of hours of...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - Prob. 23ECh. 9.1 - Home Prices According to the almanac, the average...Ch. 9.1 - Exam Scores at Private and Public Schools A...Ch. 9.1 - Sale Prices for Houses The average sales price of...Ch. 9.1 - Average Earnings for College Graduates The average...Ch. 9.2 - Too Long on the Telephone A company collects data...Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - Prob. 9ECh. 9.2 - Find the 95% confidence interval for the...Ch. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Ages of Homes Whiting, Indiana, leads the Top 100...Ch. 9.2 - Prob. 17ECh. 9.2 - Out-of-State Tuitions The out-of-state tuitions...Ch. 9.2 - Gasoline Prices A random sample of monthly...Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.3 - Air Quality As a researcher for the EPA, you have...Ch. 9.3 - Classify each as independent or dependent samples....Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - Toy Assembly Test An educational researcher...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - Prob. 13ECCh. 9.4 - Smoking and Education You are researching the...Ch. 9.4 - Prob. 1ECh. 9.4 - Find p and q for each. a. n = 36, X = 20 b. n =...Ch. 9.4 - Prob. 3ECh. 9.4 - Find each X, given p. a. p = 0.24, n = 300 b. p =...Ch. 9.4 - Prob. 5ECh. 9.4 - Find p and q. a. 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