Is achieving a basic skill level related to the location of the school? The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At $\alpha = 0.05$, test the hypothesis that the variables are independent. Complete parts (a) through (d). Location Reading Math Science Urban 48 40 43 Suburban 67 70 61 (a) Identify the claim and state the null and alternative hypotheses. $H_0$: Skill level in a subject is location. $H_1$: Skill level in a subject is location. The is the claim. (b) Calculate the test statistic. If convenient, use technology. $\chi^2 \approx$ (Round to three decimal places as needed.) (c) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Choose the correct conclusion below. A. Fail to reject the null hypothesis. There is not enough evidence to reject the claim that skill level in a subject is independent of location. B. Reject the null hypothesis. There is not enough evidence to reject the claim that skill level in a subject is independent of location. C. Fail to reject the null hypothesis. There is enough evidence to reject the claim that skill level in a subject is independent of location. D. Reject the null hypothesis. There is enough evidence to reject the claim that skill level in a subject is independent of location.
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The alternative hypotheses in this scenario are related to the location of the school. The text mentions three alternative hypotheses: a) the cam, b) c.ff convenient, use technology, and c) Abes as needed. Show more…
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If we reject a null hypothesis of "no difference" at the 0.05 level a. the odds are 20 to 1 in our favor that we have made a correct decision b. the null hypothesis is true. c. the odds are 5 to 1 in our favor that we have made a correct decision. d. the research hypothesis is true. In most cases, a researcher sets out to a. prove the null hypothesis. b. disprove the null hypothesis. c. prove the research hypothesis. d. disprove the research hypothesis. If we reject a null hypothesis which is in fact true, we a. have made a correct decision. b. have made a Type I error. c. have made a Type II error. d. should have used a one-tailed test.
Sri K.
Problem 1. Determine if each of the following statements about hypothesis testing is true or false. (a) (5 pts) Large type II error probability implies that the probability of Ho being true is small. (b) (5 pts) Let S be a test statistic and the corresponding critical region be given by S > t. Then it is possible to reduce both the probability of the type I error and the probability of the type II error by using another threshold t. (c) (5 pts) A small p-value indicates how unlikely the observation is given the null hypothesis Ho being true. (d) (5 pts) If the null hypothesis and alternative hypothesis are both simple, then the critical region of the Likelihood Ratio Test (LRT) may not be a most powerful critical region. (e) (5 pts) For a sample that results P-value=0.02, we reject the null hypothesis at any level ̑ > 0.02.
For each problem, select the best response. (a) The null hypothesis is A. the probability of observing the data you actually obtained B. a statement that the data are all 0. C. the same thing as the ''research hypothesis.'' D. assumed to be true unless substantial evidence to the contrary is presented. (b) The p -value of a hypothesis test is A. the probability the null hypothesis is false. B. the probability the null hypothesis is true. C. The probability of observing evidence in favor of the alternative hypothesis as strong or stronger than that which was observed if the null hypothesis were true. D. The probability of observing evidence in favor of the null hypothesis as strong or stronger than that which was observed if the alternative hypothesis were true. (c) In testing hypotheses, which of the following would tend to be evidence in favor of the alternative hypothesis? A. A large p -value. B. A small p -value. C. A small level of significance. D. A large level of significance.
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