The mean family income for a random sample of 600 suburban households in Loganville shows that a 95 percent confidence interval is ($43,100, $59,710). Alma is conducting a test of the null hypothesis Ho: μ =42,000 against the alternative hypothesis Ha: μ # 42,000 at the a = 0.05 level of significance. Does Alma have enough information to conduct a test of the null hypothesis against the alternative?O No, because the value of o is not knownO No, because it is not known whether the data are Normally distributedO No, because the entire data set is needed to do this testO Yes, because $42,000 is not contained in the 95% confidence interval, the null hypothesis would not be rejected, and it could be concluded that the mean family income is not significantly different from$42,000 at the a = 0.05 levelO Yes, because $42,000 is not contained in the 95% confidence interval, the null hypothesis would be rejected in favor of the alternative, and it could be concluded that the mean family income is significantlydifferent from $42,000 at the a = 0.05 level

The given data is as follows:Sample size, Confidence level, The confidence interval is .The…

Answered: The mean family income for a random…

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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Suppose that you are testing the following hypotheses: Ho: p = .80 and Ha: p # .80. You calculate a test statistic value of z = -6.08. True or False: At a 95% confidence level, which is alpha = .05, you should reject the null hypothesis. True False
Test the claim that the mean GPA of night students is smaller than 2.8 at the .05 significance level. The null and alternative hypothesis would be: = 2.8 Ho:p= 0.7 Ho:μ = 2.8 : Ho p= 0.7 Ho:μ = 2.8 Ho: p = 0.7 Ho:μ = H₁:p 2.8 H₁:p 0.7 H₁:μ 0.7 H₁:μ ‡ 2.8 The test is: right-tailed two-tailed left-tailed Based on a sample of 50 people, the sample mean GPA was 2.75 with a standard deviation of 0.02 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 hypothesis
a. What are the null and alternative hypotheses? b. The test statistic, t, is c. The P-value is d. State the conclusion for the test. e. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.
An educational psychologist studies the effect of frequent testing on retention of class material. In one of the professor's sections, students are given quizzes each week. The second section receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test with α = .01. Include the null hypothesis in symbols, critical region(s), and a conclusion about significance. Compute r2 and state the size of the effect (e.g. small, medium, large). Frequent Quizzes Two Exams n = 15 n = 15 M = 72 SS= 112 M = 68 SS= 98
Test the claim that the mean GPA of night students is significantly different than 2.2 at the 0.01 significance level. The null and alternative hypothesis would be: Ho: p = 0.55 H₁: p > 0.55 Ho : μ = 2.2 H₁ : µ 2.2 Ho:|=2.2 H₁: μ2.2 O Ho: p = 0.55 H₁: p0.55 O Ho: p = 0.55 H₁: p < 0.55 Based on a sample of 80 people, the sample mean GPA was 2.22 with a standard deviation of 0.06 The test statistic is decimals) The positive critical value is Based on this we (to 3 decimals) reject the null hypothesis fail to reject the null hypothesis (to 3
Test the claim that the mean GPA of night students is larger than 2.3 at the .025 significance level. The null and alternative hypothesis would be: Но : р — 2.3 Но:н — 2.3 Но:р %3D 0.575 Но: д —— 2.3 Но:р %3D 0.575 Но:р 3 0.575 H:р + 2.3 Hi:p 2.3 Н:р#0.575 H:р> 0.575 The test is: left-tailed right-tailed two-tailed Based on a sample of 65 people, the sample mean GPA was 2.34 with a standard deviation of 0.06 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
Which of the following statements is true regarding the influence of a small alpha level in the context of hypothesis testing? a. A small alpha level reduces the likelihood of a Type I error. b. A small alpha level reduces the effect size. c. A small alpha level increases statistical power. d. A small alpha level increases the likelihood of detecting statistical significance.
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?
Test the claim that the mean GPA of night students is larger than 2.5 at the 0.005 significance level.The null and alternative hypothesis would be: H0:p=0.625H0:p=0.625H1:p≠0.625H1:p≠0.625 H0:μ=2.5H0:μ=2.5H1:μ≠2.5H1:μ≠2.5 H0:p≤0.625H0:p≤0.625H1:p>0.625H1:p>0.625 H0:μ≤2.5H0:μ≤2.5H1:μ>2.5H1:μ>2.5 H0:p≥0.625H0:p≥0.625H1:p<0.625H1:p<0.625 H0:μ≥2.5H0:μ≥2.5H1:μ<2.5H1:μ<2.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 75 people, the sample mean GPA was 2.51 with a standard deviation of 0.05The 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 hypothesis
It has been reported in the past that the probability that an individual will develop schizophrenia over their lifetime is 0.004. A researcher believes that this proportion has increases since then. She found out that in a random sample of 2500 individuals, 16 developed schizophrenia. Is there evidence to support the claim that the true proportion of people who will develop schizophrenia is greater 0.004? Use hypothesis testing at a = 0.10 level of significance to answer this question. a. State the null and alternative hypotheses. b. What is the probability model (underlying distribution of the sample proportion p)? c. Compute p. d. Compute the test statistic. e. Find the P-value. f. Make the decision whether to reject Ho or not. g. State a conclusion answering the question above. 1
A test of the null hypothesis Ho: p = .25 gives a test statistic z = 1.6. What is the p-value if the alternative is Ha: p > .25? What is the p-value if the alternative is Ha: p < .25? What is the p-value if the alternative is Ha: p .25?

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