UNDERSTANDING BASIC STAT LL BUND >A< F
UNDERSTANDING BASIC STAT LL BUND >A< F
7th Edition
ISBN: 9781337372763
Author: BRASE
Publisher: Cengage Learning
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Chapter 10.3, Problem 5P

(a)

To determine

To find: The pooled probability of success for the two experiments.

(a)

Expert Solution
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Answer to Problem 5P

Solution: The pooled probability of success is p¯=0.66andq¯=0.34.

Explanation of Solution

Calculation: Using, r1=45,n1=75,r2=70,n2=100

Now, the pooled probability of success is calculated as follows:

p¯=r1+r2n1+n2p¯=45+7075+100p¯=0.66

Thus, the probability of success is 0.66.

Now the value of the q¯ is

q¯=1-p¯q¯=1-0.66q¯=0.34

Thus, the probability of failure is 0.34.

(b)

To determine

Whether we should use normal distribution or not.

(b)

Expert Solution
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Answer to Problem 5P

Solution: The sample test statistic follows standard normal distribution.

Explanation of Solution

The number of binomial trials is large enough that each of the products n1p¯,n1q¯,n2p¯,n2q¯ is greater than 5. Thus, it is appropriate to use standard normal distribution.

(c)

To determine

The null and alternate hypothesis.

(c)

Expert Solution
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Answer to Problem 5P

Solution: The hypotheses are H0:p¯1-p¯2=0andH1:p¯1-p¯20

Explanation of Solution

Since, we want to conduct a test of the claim that the probability of success of the two binomial experiments are differ. Therefore, the null hypothesis is H0:p¯1-p¯2=0 v/s alternative hypothesis is H1:p¯1-p¯20.

(d)

To determine

To find: The difference of sample proportion p¯1-p¯2 and the corresponding sample test statistic.

(d)

Expert Solution
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Answer to Problem 5P

Solution: The difference of sample proportion p¯1-p¯2 is - 0.1 and the corresponding sample test statistic is z = -1.42.

Explanation of Solution

Calculation:

The difference of p¯1-p¯2 is calculated as follows:

p^1-p^2=r1n1-r2n2p^1-p^2=4575-70100p^1-p^2=-0.1

Thus, thedifference of sample proportion p¯1-p¯2 is - 0.1

The sample test statistic is calculated as follows:

z=p^1-p^2p¯q¯n1+p¯q¯n2z=-0.10.66*0.3475+0.66*0.34100z=-1.42

Thus, the sample test statistic is -1.42.

(e)

To determine

To find: The P-value of the sample test statistic.

(e)

Expert Solution
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Answer to Problem 5P

Solution: The P-value of test statistic is approximately 0.1556.

Explanation of Solution

Calculation:

The P-value is calculated as follows:

P-value=Areatotheleftof1.42+Area to the right of 1.42P-value=P(z<-1.42)+P(z>1.42)P-value=2P(z<-1.42)

Using table 3 from Appendix, we get

P-value=2(0.0778)P-value=0.1556

Thus the P-value of the sample test statistic is approximately 0.1556.

(f)

To determine

Whether we should reject or fail to reject the null hypothesis for a 5% level of significance.

(f)

Expert Solution
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Answer to Problem 5P

Solution: The P-value > α, hence we have failed to reject H0.

Explanation of Solution

The P-value is greater than the level of significance (α) of 0.05. Therefore we don’t have enough evidence to reject the null hypothesis H0 i.e. the P-value is not statistically significant.

(g)

To determine

Interpretation for the result.

(g)

Expert Solution
Check Mark

Answer to Problem 5P

Solution: We have insufficient evidence in the favor of the claim the probability of success for the two binomial experiments are different from each other.

Explanation of Solution

The P-value is greater than the level of significance (α) of 0.05. Therefore, we don’t have enough evidence to reject the null hypothesis H0 i.e. the P-value is not statistically significant. We have insufficient evidence in the favor of the claim the probability of success for the two binomial experiments are different from each other.

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Chapter 10 Solutions

UNDERSTANDING BASIC STAT LL BUND >A< F

Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - Prob. 14PCh. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - Prob. 17PCh. 10.1 - Expand Your Knowledge: Confidence Intervals for d...Ch. 10.1 - Prob. 19PCh. 10.1 - Prob. 20PCh. 10.2 - Statistical Literacy Consider a hypothesis test of...Ch. 10.2 - Prob. 2PCh. 10.2 - Prob. 3PCh. 10.2 - Prob. 4PCh. 10.2 - Critical Thinking Josh and Kendra each calculated...Ch. 10.2 - Critical Thinking If a 90% confidence interval for...Ch. 10.2 - Basic Computation: Paired Differences Test For a...Ch. 10.2 - Basic Computation: Texting 12 Two populations have...Ch. 10.2 - Basic Computation: Testing- 12 A random sample of...Ch. 10.2 - Basic Computation: Testing 12 Two populations have...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Prob. 21PCh. 10.2 - Prob. 22PCh. 10.2 - Prob. 23PCh. 10.2 - Prob. 24PCh. 10.2 - Prob. 25PCh. 10.2 - Critical Region Method: Testing 12;1,2Known Redo...Ch. 10.3 - Statistical Literacy Consider a hypothesis test of...Ch. 10.3 - Statistical Literacy Consider a hypothesis test of...Ch. 10.3 - Critical Thinking Consider two independent...Ch. 10.3 - Critical Thinking If a 90% confidence interval for...Ch. 10.3 - Prob. 5PCh. 10.3 - Basic Computation: Testing p1p2 For one binomial...Ch. 10.3 - Federal Tax Money: Art Funding Would you favor...Ch. 10.3 - Art Funding: Politics Would you favor spending...Ch. 10.3 - Sociology: Trusting People Generally speaking,...Ch. 10.3 - Political Science: Voters This problem is based on...Ch. 10.3 - Extraterrestrials: Believe It? Based on...Ch. 10.3 - Art: Polities Do you prefer paintings in which the...Ch. 10.3 - Prob. 13PCh. 10.3 - Critical Region Method: Testing p1p2 Redo Problem...Ch. 10.3 - Basic Computation: Confidence Inters al for p1p2...Ch. 10.3 - Prob. 16PCh. 10.3 - Myers-Briggs: Marriage Counseling Isabel Myers was...Ch. 10.3 - Myers-Briggs: Marriage Counseling Most married...Ch. 10.3 - Navajo Culture: Traditional Hogans S. C. Jett is a...Ch. 10.3 - Archaeology: Cultural Affiliation "Unknown...Ch. 10.3 - Critical Thinking: Different Confidence Levels (a)...Ch. 10.3 - Focus Problem: Wood Duck Nests In the Focus...Ch. 10 - Statistical Literacy and Terminology When are two...Ch. 10 - 2. Statistical Literacy and Terminology When are...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - Prob. 8CRCh. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - Prob. DHGPCh. 10 - In there a relationship between confidence...
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