Understanding Basic Statistics
Understanding Basic Statistics
8th Edition
ISBN: 9781337558075
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 11.1, Problem 18P

(i)

To determine

To graph: A cluster bar graph showing the percentages of Congress members from each party who spent each designated amount in their respective home districts.

(i)

Expert Solution
Check Mark

Explanation of Solution

Calculation: To find the percentage table:

Party Less than 5 Billion 5 to 10 Billion More than 10 Billion
Democratic 845×10018 1545×10033 2245×10049
Republican 1247×10026 1947×10040 1647×10034

Graph: To create cluster bar graph by using Excel is as follows:

Step 1: Enter the percentage data table in Excel worksheet.

Step 2: Select table and go to Insert > Charts > Column.

The cluster bar graph is obtained as:

Understanding Basic Statistics, Chapter 11.1, Problem 18P

(ii)

(a)

To determine

The level of significance and state the null and alternative hypotheses.

(ii)

(a)

Expert Solution
Check Mark

Answer to Problem 18P

Solution: The level of significance is 0.01. H0: Same proportion of Democrats and Republicans within each spending level, H1: Different proportion of Democrats and Republicans within each spending level.

Explanation of Solution

The level of significance, α=0.01.

The null hypothesis for testing is defined as,

H0: Same proportion of Democrats and Republicans within each spending level.

The alternative hypothesis is defined as,

H1: Different proportion of Democrats and Republicans within each spending level.

(b)

To determine

To test: Whether all the expected frequencies are greater than 5. Also determine the value of chi-square statistic for the sample, the sampling distribution that should be used and degrees of freedom for the test.

(b)

Expert Solution
Check Mark

Answer to Problem 18P

Solution: The value of chi-square statistic for the sample, χ2=2.176, expected frequencies are greater than 5, we should use chi-square distribution and degrees of freedom are 2.

Explanation of Solution

Calculation: The find the χ2 statistic for the sample by using MINITAB software is as:

Step 1: Go to Stat >Tables> Chi-square Test For Association.

Step 2: Select ‘Summarized data in two-way table’ and select <5B, 5-10B, >10Bin ‘Columns containing the table’ box.

Step 3: Select ‘Partyin ‘Rows’ and write any name in ‘Columns’ and click on ‘Statistics’ tick on Chi-square test and Expected cell counts. Then click on OK.

The Minitab output is:

Chi-Square Test for Association: Party, spent

Rows: Party   Columns: spent

<5B 5-10B >10B
       
Democratic 9.78 16.63 18.59
Republican 10.22 17.37 19.41

Cell Contents

      Expected count

Chi-Square Test

Chi-Square DF P-Value
Pearson 2.176 2 0.337
Likelihood Ratio 2.185 2 0.335

Therefore, the obtained Chi-square test statistics is 2.176.

The obtained expected frequencies are:

Party <5B 5-10B >10B
Democratic 9.78 16.63 18.59
Republican 10.22 17.37 19.41

So, all expected frequencies are greater than 5.

The chi-square distribution should be used in this study and the obtained degrees of freedom are 2.

(c)

To determine

The P-value of the sample statistic.

(c)

Expert Solution
Check Mark

Answer to Problem 18P

Solution: The P-value of sample statistic is 0.337.

Explanation of Solution

Calculation: The Minitab output obtained in above part (b) also gives the P-value. So, the P-value for the sample test statistic is 0.337.

(d)

To determine

To explain: Whether we will reject or fails to reject the null hypothesis.

(d)

Expert Solution
Check Mark

Answer to Problem 18P

Solution: We failed to reject the null hypothesis at significance level 0.05.

Explanation of Solution

The obtained results in part (a), (b) and (c) are,

α=0.01

χ2statistic=2.176 with 2 degrees of freedom.

Since the P-value (0.337) is greater than 0.01, hence we failed to reject the null hypothesis of independence at α=0.01. Therefore it is concluded that the data are not statistically significant at 0.01 level of significance.

(e)

To determine

To explain: The conclusion in the context of application.

(e)

Expert Solution
Check Mark

Answer to Problem 18P

Solution: It is concluded that the Stone tools construction material and sitearenot independent.

Explanation of Solution

From above part, it can be seen that we failed to reject the null hypothesis at α=0.01 and we can conclude that the data are not statistically significant.

Therefore, at the 1% level of significance, there is sufficient evidence to conclude that congressional members of each political party spent designated amounts in the same proportions.

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Chapter 11 Solutions

Understanding Basic Statistics

Ch. 11.1 - For Problems 9-19, please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - For Problems 9-19. please provide the following...Ch. 11.1 - Prob. 17PCh. 11.1 - Prob. 18PCh. 11.1 - Prob. 19PCh. 11.2 - Statistical Literacy For a chi-square...Ch. 11.2 - Statistical Literacy How are expected frequencies...Ch. 11.2 - Statistical Literacy Explain why goodness-of-fit...Ch. 11.2 - Critical Thinking When the sample evidence is...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - Prob. 10PCh. 11.2 - Prob. 11PCh. 11.2 - For Problems 5-14, please provide the following...Ch. 11.2 - Prob. 13PCh. 11.2 - Prob. 14PCh. 11.2 - Prob. 15PCh. 11.2 - For Problems 5-14, please provide the following...Ch. 11.3 - Statistical Literacy Docs the x distribution need...Ch. 11.3 - Prob. 2PCh. 11.3 - Prob. 3PCh. 11.3 - For Problems 3-11, please provide the following...Ch. 11.3 - For Problems 3-11. please provide the following...Ch. 11.3 - For Problems 3-11. please provide the following...Ch. 11.3 - Prob. 7PCh. 11.3 - For Problems 3-11, please provide the following...Ch. 11.3 - For Problems 3-11. please provide the following...Ch. 11.3 - Prob. 10PCh. 11.3 - Prob. 11PCh. 11.4 - Prob. 1PCh. 11.4 - Statistical Literacy What is the symbol used for...Ch. 11.4 - Prob. 3PCh. 11.4 - Statistical Literacy How does the t value for the...Ch. 11.4 - Prob. 5PCh. 11.4 - Using Computer Printouts Problems 5 and 6 use the...Ch. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - In Problems 7-12, parts (a) and (b) relate to...Ch. 11.4 - Prob. 11PCh. 11.4 - Prob. 12PCh. 11.4 - Prob. 13PCh. 11.4 - Prob. 14PCh. 11.4 - Prob. 15PCh. 11.4 - Prob. 16PCh. 11.4 - Prob. 17PCh. 11.4 - Prob. 18PCh. 11.4 - Prob. 19PCh. 11 - Terminology Match each of the following tests to...Ch. 11 - Prob. 2CRCh. 11 - Statistical Literacy of the following random...Ch. 11 - Prob. 4CRCh. 11 - Prob. 5CRCh. 11 - Before you solve Problems 6-10, first classify the...Ch. 11 - Prob. 7CRCh. 11 - Before you solve Problems 6-10, first classify the...Ch. 11 - Before you solve Problems 6-10, first classify the...Ch. 11 - Prob. 10CRCh. 11 - Prob. 11CRCh. 11 - Prob. 12CRCh. 11 - Prob. 13CRCh. 11 - Prob. 14CRCh. 11 - Prob. 15CRCh. 11 - The Statistical Abstract of the United States...Ch. 11 - Prob. 1LCWPCh. 11 - Prob. 2LCWPCh. 11 - Prob. 3LCWPCh. 11 - Prob. 4LCWPCh. 11 - Prob. 1CRPCh. 11 - Prob. 2CRPCh. 11 - Prob. 3CRPCh. 11 - Prob. 4CRPCh. 11 - Prob. 5CRPCh. 11 - Prob. 6CRPCh. 11 - Prob. 7CRP
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