**Chapter 10 End-of-Chapter Problems****4. Gravetter/Wallnau/Forzano, - Chapter 10 - End-of-chapter question 7**Research results suggest a relationship between the TV viewing habits of 5-year-old children and their future performance in high school. For example, Anderson, Huston, Wright, and Collins (1998) report that high school students who regularly watched *Sesame Street* as children had better grades in high school than their peers who did not watch *Sesame Street*.Suppose that a researcher intends to examine this phenomenon using a sample of 20 high school students. The researcher first surveys the students’ parents to obtain information on the family’s TV viewing habits during the time that the students were 5 years old. Based on the survey results, the researcher selects a sample of n = 10 students with a history of watching *Sesame Street* and a sample of n = 10 students who did not watch the program. The average high school grade is recorded for each student, and the data are as follows:**Table: Average High School Grade**| Watched Sesame Street | Did Not Watch Sesame Street ||-----------------------|-----------------------------|| 86 | 79 || 87 | 83 || 91 | 86 || 97 | 81 || 98 | 92 || **n = 10** | **n = 10** || **M = 93** | **M = 85** || **SS = 200** | **SS = 160** |- **M (Mean):** Represents the average score for each group.- **SS (Sum of Squares):** Indicates the total squared deviation from the mean.This data suggests a potential relationship between early childhood TV viewing habits and later academic performance. ## Chapter 10 End-of-Chapter Problems### QuestionIs there a significant difference in reported performance between the two groups of students? Use an independent-measures two-tailed test with α = 0.01.### Inputs Required- **t-critical = ±** [Input box with dropdown]- **t =** [Input box with dropdown]### Options- ○ Reject the null hypothesis; there is a significant difference.- ○ Fail to reject the null hypothesis; there is no significant difference.- ○ Reject the null hypothesis; there is no significant difference.- ○ Fail to reject the null hypothesis; there is a significant difference.---### Diagram Explanation#### t Distribution Chart- **Graph Description:** The graph shows a symmetric bell-shaped curve representing the t distribution.- **Degrees of Freedom Slider:** Adjust the degrees of freedom for the distribution, currently set to 21.- **Graph Highlights:** - The curve is shaded, indicating the critical regions where the null hypothesis would be rejected.This interactive chart helps determine the critical t values based on the degrees of freedom, which are essential for hypothesis testing.

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Answered: Is there a significant difference in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .005 significance level. The null and alternative hypothesis would be: Ho: PM = PF Ho: MM = F Ho: PM = PF H₁ PM PF H₁: μM μF H₁ PM > PF O O The test is: left-tailed two-tailed O O Based on a sample of 80 men, 25% owned cats Based on a sample of 20 women, 35% owned cats The test statistic is: The p-value is: right-tailed O Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis Ho: PM = MF H₁: MM > MF (to 2 decimals) (to 2 decimals) Ho: MM = F Ho:PM = PF H₁: MM < MF H₁:PM < PF O O
Test the claim that the proportion of men who own cats is larger than 50% at the .025 significance level. The null and alternative hypothesis would be: Ho p= 0.5 Ho: μ = Ho : μ Ho: p = 0.5 o H₁ μ> H₁ μ‡ H₁: p 0.5 : Ho p= 0.5 H₁ μ = H₁ p0.5 H₁:μ< The test is: right-tailed left-tailed two-tailed Based on a sample of 65 men, The test statistic is: z = (to 2 decimals) The critical value is ZC =1.95996. Thus the test statistic (is critical region. 4265 Based on this we: of the men owned cats Fail to reject the null hypothesis Reject the null hypothesis in the
Test the claim that the mean GPA of night students is larger than 2.8 at the .10 significance level. The null and alternative hypothesis would be: Ho: p=0.7 Ho: p = 0.7 Ho:μ = 2.8 Ho: H₁:p> 0.7 H₁:p 2.8 H₁: The test is: left-tailed two-tailed right-tailed o The test statistic is: 2.8 Ho:p = 0.7 Ho:μ = 2.8 0 <2.8 H₁:p 0.7 H₁: 2.8 Based on a sample of 40 people, the sample mean GPA was 2.83 with a standard deviation of 0.02 (to 2 decimals) The critical value is: = (to 2 decimals)
B. Identify the test statistic. ______ C. Identify the P-value. ____ D. What is the conclusion for this test? The P-value is (greater than/less than) the significance level α, so (reject/ fail to reject) the null hypothesis. There is (sufficient/ insufficient) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
Test the claim that the mean GPA of night students is smaller than 2.2 at the 0.025 significance level. The null and alternative hypothesis would be: Ho: 2.2 Ho:p ≤ 0.55 Ho:p≥ 0.55 Ho:p = 0.55 Ho:μ = 2.2 Ho:μ ≤ 2.2 H₁: 0.55 H₁:p 2.2 The test is: two-tailed left-tailed right-tailed Based on a sample of 35 people, the sample mean GPA was 2.15 with a standard deviation of 0.04 The p-value is: Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis (to 2 decimals)
Test the claim that the mean GPA of night students is larger than 3.1 at the 0.01 significance level. The null and alternative hypothesis would be: Но: р — 0.775 Но:р> 0.775 Но: и — 3.1 Но:р 3.1 Н:р+ 0.775 Hi:р 3.1 H]:p > 0.775 Hi:р < 3.1 The test is: right-tailed two-tailed left-tailed Based on a sample of 80 people, the sample mean GPA was 3.14 with a standard deviation of 0.07 The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis
Test the claim that the mean GPA of night students is larger than 2.4 at the 0.025 significance level. The null and alternative hypothesis would be: Ho: µ = — 2.4 Но:р 2.4 Н: + 2.4 H:p> 0.6 H:д> 2.4 Hi:p #0.6 Hi:p < 0.6 Н:р < 2.4 The test is: left-tailed two-tailed right-tailed Based on a sample of 65 people, the sample mean GPA was 2.41 with a standard deviation of 0.03 The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis
In testing hypotheses, which of the following provides strong evidence against the null hypothesis? Using a small level of significance a Using a large level of significance Obtaining data with a small P-value O d Obtaining data with a large P-value
Test the claim that the proportion of men who own cats is larger than 20% at the .05 significance level. The null and alternative hypothesis would be: 0.2 Но:р — 0.2 Но: и 0.2 Ho:H Ho:H H:р + 0.2 Н]:р 0.2 Hi:р > 0.2 Hi:р#0.2 0.2 Но:р || The test is: left-tailed two-tailed right-tailed Based on a sample of 25 people, 25% owned cats The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis
Test the claim that the proportion of people who own cats is significantly different than 40% at the 0.2 significance level. The null and alternative hypothesis would be: Ho:p 0.4 Ho: u 2 0.4 Ho:p = 0.4 Ho: p = 0.4 Ho:u 0.4 H1:p 0.4 The test is: two-tailed left-tailed right-tailed Based on a sample of 700 people, 34% owned cats The p-value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis Question Help: DVideo M hp
You are interested in investigating whether gender and major are associated at your college. The table below shows the results of a survey. Math/Science Arts/Humanities Business/Econ. Other Men 76 109 73 49 Women 82 96 93 34 What can be concluded at the αα = 0.01 significance level? What is the correct statistical test to use? Independence Homogeneity Goodness-of-Fit Paired t-test What are the null and alternative hypotheses?H0:H0: The distribution of college major is the same for each gender. College major and gender are independent. College major and gender are dependent. The distribution of college major is not the same for each gender. H1:H1: College major and gender are independent. The distribution of college major is not the same for each gender. College major and gender are dependent. The distribution of college major is the same for each gender. The test-statistic for this data = (Please show your answer to three decimal places.) The p-value for…
A psychologist specializing counseling claims that, among all married couples, the proportion p for whom her communication program can prevent divorce 79% . In a random sample of 240 married couples who completed her program, 174 of them stayed together. Based on this sample, can we reject the psychologist's claim at the 0.1 level of significance The null hypothesis: H0: ___ The alternative hypothesis: H1: ___ The type of test statistic: (Choose one) ___ The value of the test statistic: (Round to at least three decimal places.) ______ The p-value: (Round to at least three decimal places.) _____ Can we reject psychologist’s claim that the Proportion of married couples for whom her Program can prevent divorce is a least 79%? Yes ____ or NO____

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