Statistical Reasoning for Everyday Life (5th Edition)
5th Edition
ISBN: 9780134494043
Author: Jeff Bennett, William L. Briggs, Mario F. Triola
Publisher: PEARSON
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Chapter 10.2, Problem 15E
a.
To determine
Define the null and alternative hypotheses.
b.
To determine
Find the expected frequency for each cell of the table assuming that two variables are independent.
c.
To determine
Compute the value of the
d.
To determine
Compute the critical value of
e.
To determine
Draw the conclusions from the hypothesis test about whether the two variables are independent.
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Test the claim that the proportion of people who own cats is smaller than 50% at the 0.01 significance level.The null and alternative hypothesis would be:
H0:p≥0.5H0:p≥0.5Ha:p<0.5Ha:p<0.5
H0:μ=0.5H0:μ=0.5Ha:μ≠0.5Ha:μ≠0.5
H0:μ≤0.5H0:μ≤0.5Ha:μ>0.5Ha:μ>0.5
H0:p≤0.5H0:p≤0.5Ha:p>0.5Ha:p>0.5
H0:p=0.5H0:p=0.5Ha:p≠0.5Ha:p≠0.5
H0:μ≥0.5H0:μ≥0.5Ha:μ<0.5Ha:μ<0.5
The test is:
left-tailed
two-tailed
right-tailed
Based on a sample of 100 people, 49% owned catsThe test statistic is: (Round to 2 decimals)The p-value is: (Round to 2 decimals)Based on this we:
The proportion of mango trees on an island that produce only dwarf fruit is p1. The proportion of mango trees on a different island that produce only dwarf fruit is p2. What is the null hypothesis for a test to determine if the proportions are different between the two islands?
Select the correct answer below:
H0: p1−p2≠0
H0: p1−p2=0
H0: p1−p2>0
H0: p1−p2<0
At many college bookstores, students can decide whether to purchase or to rent a textbook for a class. A study was conducted to investigate whether the percent of rented textbooks for all science classes in the state was greater than the percent of rented textbooks for all literature classes in the state. The following hypothesis test was done at the significance level of α=0.05α=0.05.
H0:pS=pLHa:pS>pLH0:pS=pLHa:pS>pL
In the hypotheses, pSpS represents the proportion of all science textbooks that are rented, and pLpL represents the proportion of all literature textbooks that are rented.
All conditions for inference were met, and the resulting pp-value was 0.035. Which of the following is the correct decision for the test?
The pp-value is less than αα. Since 0.035<0.050.035<0.05, the null hypothesis is rejected, and the claim is supported. There is convincing statistical evidence that the proportion of all science textbooks that are rented is greater…
Chapter 10 Solutions
Statistical Reasoning for Everyday Life (5th Edition)
Ch. 10.1 - t Distribution. What is the t distribution? What...Ch. 10.1 - Degrees of Freedom. How do you determine the...Ch. 10.1 - Prob. 3ECh. 10.1 - Hypothesis Test. Briefly summarize the procedure...Ch. 10.1 - Does It Make Sense? For Exercises 58, determine...Ch. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Confidence Intervals. In Exercises 918, use the t...Ch. 10.1 - Confidence Intervals. In Exercises 918, use the t...
Ch. 10.1 - Elbow-to-Fingertip Length of Men. A simple random...Ch. 10.1 - Earthquake Epicenter Depths. A simple random...Ch. 10.1 - Hospital Costs with Seat Belts. A study was...Ch. 10.1 - Prob. 14ECh. 10.1 - Estimating Car Pollution. Each car in a sample of...Ch. 10.1 - Movie Lengths. Listed below are lengths (in...Ch. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Hypothesis Tests. In Exercises 1928, test the...Ch. 10.1 - Prob. 20ECh. 10.1 - Hypothesis Tests. In Exercises 1928, test the...Ch. 10.1 - Prob. 22ECh. 10.1 - Hypothesis Tests. In Exercises 1928, test the...Ch. 10.1 - Hypothesis Tests. In Exercises 1928, test the...Ch. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.2 - Two-Way Tables. What is a two-way table? What are...Ch. 10.2 - Hypotheses. When working with two variables in a...Ch. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Does It Make Sense? For Exercises 58, determine...Ch. 10.2 - Does It Make Sense? For Exercises 58, determine...Ch. 10.2 - Does It Make Sense? For Exercises 58, determine...Ch. 10.2 - Does It Make Sense? For Exercises 58, determine...Ch. 10.2 - Prob. 9ECh. 10.2 - Understanding a Two-Way Table Hypothesis Test....Ch. 10.2 - Survey Results. In Exercises 1114, assume that a...Ch. 10.2 - Survey Results. In Exercises 1114, assume that a...Ch. 10.2 - Survey Results. In Exercises 1114, assume that a...Ch. 10.2 - Survey Results. In Exercises 1114, assume that a...Ch. 10.2 - Prob. 15ECh. 10.2 - Complete Hypothesis Test. In Exercises 1522, carry...Ch. 10.2 - Complete Hypothesis Test. In Exercises 1522, carry...Ch. 10.2 - Complete Hypothesis Test. In Exercises 1522, carry...Ch. 10.2 - Complete Hypothesis Test. In Exercises 1522, carry...Ch. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.3 - ANOVA. What does ANOVA stand for? What is the...Ch. 10.3 - Prob. 2ECh. 10.3 - Variance in ANOVA. Describe and distinguish...Ch. 10.3 - Test Statistic F. What is the meaning of small and...Ch. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Does It Make Sense? For Exercises 58, determine...Ch. 10.3 - Does It Make Sense? For Exercises 58, determine...Ch. 10.3 - Prob. 9ECh. 10.3 - Comparing Colleges. A researcher obtains random...Ch. 10.3 - Readability of Authors. Samples of Flesch-Kincaid...Ch. 10.3 - Fabric Flammability Tests in Different...Ch. 10.3 - Prob. 13ECh. 10.3 - Pulse Rates. A random sample of adult females is...Ch. 10.3 - Using Technology. In Exercises 1518, use software...Ch. 10.3 - Using Technology. In Exercises 1518, use software...Ch. 10.3 - Prob. 17ECh. 10.3 - Using Technology. In Exercises 1518, use software...Ch. 10 - In Exercises 13, use the following service times...Ch. 10 - In Exercises 13, use the following service times...Ch. 10 - In Exercises 13, use the following service times...Ch. 10 - Prob. 4CRECh. 10 - Prob. 1CQCh. 10 - As part of the results from the test described in...Ch. 10 - For the hypothesis test described in Exercise 1,...Ch. 10 - A simple random sample of 25 blood platelet counts...Ch. 10 - Prob. 5CQCh. 10 - Prob. 6CQCh. 10 - Prob. 7CQCh. 10 - If the hypothesis test of the claim described in...Ch. 10 - A two-way table, constructed from survey results,...Ch. 10 - Prob. 10CQ
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- In Exercises, the null hypothesis is H0:µ1 = µ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothesis test at the 10% significance level. Ha: µ1 >µ2 Observation from Pair Population 1 Population 2 1 7 3 2 4 5 3 9 8 4 7 2 5 19 16 6 12 12 7 13 18 8 5 11arrow_forwardTest the claim that the proportion of people who own cats is smaller than 20% at the 0.005 significance level.The null and alternative hypothesis would be: Select One ______ H0:p≤0.2H0:p≤0.2Ha:p>0.2Ha:p>0.2 _______H0:μ≥0.2H0:μ≥0.2Ha:μ<0.2Ha:μ<0.2 _____H0:μ=0.2H0:μ=0.2Ha:μ≠0.2Ha:μ≠0.2 ______H0:p=0.2H0:p=0.2Ha:p≠0.2Ha:p≠0.2 _______H0:p≥0.2H0:p≥0.2Ha:p<0.2Ha:p<0.2 ______H0:μ≤0.2H0:μ≤0.2Ha:μ>0.2Ha:μ>0.2 The test is: Select One ___two-tailed ___left-tailed ___right-tailed Based on a sample of 600 people, 19% owned catsThe test statistic is: __?__ (Round to 2 decimals)The p-value is: __?__ (Round to 2 decimals)arrow_forwardTest the claim that the proportion of people who own cats is smaller than 50% at the 0.025 significance level.The null and alternative hypothesis would be: H0:p≤0.5H0:p≤0.5Ha:p>0.5Ha:p>0.5 H0:μ≥0.5H0:μ≥0.5Ha:μ<0.5Ha:μ<0.5 H0:p=0.5H0:p=0.5Ha:p≠0.5Ha:p≠0.5 H0:p≥0.5H0:p≥0.5Ha:p<0.5Ha:p<0.5 H0:μ=0.5H0:μ=0.5Ha:μ≠0.5Ha:μ≠0.5 H0:μ≤0.5H0:μ≤0.5Ha:μ>0.5Ha:μ>0.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 700 people, 43% owned catsThe test statistic is: (Round to 2 decimals)The p-value is: (Round to 2 decimals)Based on this we: Reject the null hypothesis Do not reject the null hypothesisarrow_forward
- Test the null hypothesis H0 : β1 = β2 against the alternative H1 : β1 < β2 at 1% significance level.arrow_forwardTest the claim that the proportion of people who own cats is larger than 90% at the 0.01 significance level.The null and alternative hypothesis would be: H0:μ=0.9H0:μ=0.9Ha:μ<0.9Ha:μ<0.9 H0:p=0.9H0:p=0.9Ha:p<0.9Ha:p<0.9 H0:μ=0.9H0:μ=0.9Ha:μ>0.9Ha:μ>0.9 H0:p=0.9H0:p=0.9Ha:p>0.9Ha:p>0.9 H0:p=0.9H0:p=0.9Ha:p≠0.9Ha:p≠0.9 H0:μ=0.9H0:μ=0.9Ha:μ≠0.9Ha:μ≠0.9 The test is: left-tailed right-tailed two-tailed Based on a sample of 600 people, 93% owned catsThe test statistic is: (to 2 decimals)The p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardIn each of Exercises, we have given the P-value for a hypothesis test. For each exercise, refer to Table to determine the strength of the evidence against the null hypothesis. P-value Evidence against H0 P > 0.10 Weak or none 0.05 < P ≤ 0.10 Moderate 0.01 < P ≤ 0.05 Strong P ≤ 0.01 Very strong P = 0.086arrow_forward
- Test the claim that the proportion of men who own cats is smaller than 70% at the 0.01 significance level. The null and alternative hypothesis would be: H0:μ≥0.7H0:μ≥0.7H1:μ<0.7H1:μ<0.7 H0:p≥0.7H0:p≥0.7H1:p<0.7H1:p<0.7 H0:μ≤0.7H0:μ≤0.7H1:μ>0.7H1:μ>0.7 H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7 H0:p≤0.7H0:p≤0.7H1:p>0.7H1:p>0.7 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 Correct The test is: left-tailed right-tailed two-tailed Correct Based on a sample of 300 people, 69% owned cats The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardTest the claim that the proportion of people who own cats is smaller than 10% at the 0.025 significance level.The null and alternative hypothesis would be: H0:μ≥0.1H0:μ≥0.1Ha:μ<0.1Ha:μ<0.1 H0:p≤0.1H0:p≤0.1Ha:p>0.1Ha:p>0.1 H0:μ≤0.1H0:μ≤0.1Ha:μ>0.1Ha:μ>0.1 H0:μ=0.1H0:μ=0.1Ha:μ≠0.1Ha:μ≠0.1 H0:p=0.1H0:p=0.1Ha:p≠0.1Ha:p≠0.1 H0:p≥0.1H0:p≥0.1Ha:p<0.1Ha:p<0.1 The test is: right-tailed left-tailed two-tailed Based on a sample of 600 people, 2% owned catsThe test statistic is: (Round to 2 decimals)The p-value is: (Round to 2 decimals)Based on this we: Do not reject the null hypothesis Reject the null hypothesisarrow_forwardIn each of Exercises, we have provided a null hypothesis and alternative hypothesis and a sample from the population under consideration. In each case, use theWilcoxon signed-rank test to perform the required hypothesis test at the 10% significance level. H0: µ = 10, Ha: µ<10 7 6 5 12 15 14 13 4arrow_forward
- In each of Exercises, we have provided a null hypothesis and alternative hypothesis and a sample from the population under consideration. In each case, use theWilcoxon signed-rank test to perform the required hypothesis test at the 10% significance level. H0: µ = 5, Ha: µ > 5 12 7 11 9 3 2 8 6arrow_forwardTest the claim that the mean GPA of night students is larger than 2.2 at the 0.10 significance level.The null and alternative hypothesis would be: H0:p≤0.55H0:p≤0.55HA:p>0.55HA:p>0.55 H0:μ=2.2H0:μ=2.2HA:μ≠2.2HA:μ≠2.2 H0:μ≥2.2H0:μ≥2.2HA:μ<2.2HA:μ<2.2 H0:p=0.55H0:p=0.55HA:p≠0.55HA:p≠0.55 H0:p≥0.55H0:p≥0.55HA:p<0.55HA:p<0.55 H0:μ≤2.2H0:μ≤2.2HA:μ>2.2HA:μ>2.2 The test is: left-tailed two-tailed right-tailed Based on a sample of 35 people, the sample mean GPA was 2.25 with a standard deviation of 0.03The p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardIf all other factors are held constant, which of the following results in a decrease in the probability of a Type IIII error? The true parameter is closer to the value of the null hypothesis. A The sample size is decreased. B The significance level is decreased. C The standard error is decreased. D The probability of a Type IIII error cannot be decreased, only increased. Earrow_forward
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