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- You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 65% at a level of significance of αα = 0.01. According to your sample, 37 out of 59 potential voters prefer the Democratic candidate. For this study, we should use The null and alternative hypotheses would be: Ho: (please enter a decimal) H1: (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly smaller than 65% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 65%. The data suggest the populaton proportion is significantly smaller than 65% at αα = 0.01, so…(a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. Type of test statistic: ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) and (e) At the 0.10 level, can the owner conclude that the mean daily sales of the two storesA sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the critical-value approach. Sample mean = 7.1 s = 2.3 n = 18 α = 0.01 H0: µ = 10 H1: µ < 10 The critical value(s) is/are (If there are two critical values separate each with a comma and list from smallest to largest)
- Only 12% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 351 randomly selected registered voters surveyed, 53 of them will vote in the upcoming election. What can be concluded at the αα = 0.01 level of significance? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer ≠ > = < (please enter a decimal) H1:H1: ? μ p Select an answer > ≠ < = (Please enter a decimal) The test statistic ? z t = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer reject accept fail to reject the null hypothesis. Thus, the final conclusion is thatConduct a test at the alphaαequals=0.010.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2p1>p2. The sample data are x 1 equals 128x1=128, n 1 equals 247n1=247, x 2 equals 140x2=140, and n 2 equals 311n2=311. (a) Choose the correct null and alternative hypotheses below. A. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 less than p 2H1: p1<p2 B. Upper H 0 : p 1 equals 0H0: p1=0 versus Upper H 1 : p 1 not equals 0H1: p1≠0 C. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 greater than p 2H1: p1>p2 D. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 not equals p 2H1: p1≠p2 (b) Determine the test statistic. z0equals=nothing (Round to two decimal places as needed.) (c) Determine…Building codes in southern Florida require hurricane straps on single-family dwellings in order to more securely anchor the roof to the buildings. The straps should have no more than a 10% chance of failure in 150mph wind, and no more than a 45% chance of failure in a 200mph wind. 164 straps are tested at 200mph, and 48 of them fail. (a) Perform a hypothesis test to evaluate the claim that the straps are performing to code to an α = 0.01(b) Provide the p − value for your test statistic determined in (a)(c) If you wished to construct a 95% confidence interval for the population proportion with half-width E = 0.01, approximately how many straps would you need to test?
- You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:p1=p2 Ha:p1≠p2You obtain 53% successes in a sample of size n1=481 from the first population. You obtain 54.9% successes in a sample of size n2=284 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value =A hypothesis test with a sample of n = 15 participants produces a t statistic of t = +2.72. Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision? Select one: a. The researcher can reject the null hypothesis with α = .05 but not with α = .01. b. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. c. The researcher can reject the null hypothesis with either α = .05 or α = .01. d. It is impossible to make a decision about H0 without more information.Only 15% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 363 randomly selected registered voters surveyed, 58 of them will vote in the upcoming election. What can be concluded at the αα = 0.01 level of significance? For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: H0:H0: ? μ p Select an answer > < ≠ = (please enter a decimal) H1:H1: ? μ p Select an answer = < ≠ > (Please enter a decimal) The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ αα Based on this, we should Select an answer accept reject fail to reject the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly higher than 15% at αα = 0.01, so there…
- Which of the following is the correct null hypothesis for an independent-samples t-test? μ1 – μ2 = 0 x̅1 – x̅2 = 0 μ1 – μ2 ≠ 0 x̅1 – x̅2 ≠ 0A random sample of size 64 is to be used to test thenull hypothesis that for a certain age group the mean score on an achievement test (the mean of a normal pop-ulation with σ2 = 256) is less than or equal to 40.0 against the alternative that it is greater than 40.0. If the nullhypothesis is to be rejected if and only if the mean of therandom sample exceeds 43.5, find (a) the probabilities of type I errors when μ = 37.0, 38.0,39.0, and 40.0;(b) the probabilities of type II errors when μ = 41.0, 42.0,43.0, 44.0, 45.0, 46.0, 47.0, and 48.0.Also plot the power function of this test criterion.Suppose that we need to compute the probability of Type II error and the power for the following hypothesis test: Ho: μ = 5 and H1: μ > 5 with the following decision rule: reject Ho if [-5]/[0.1/] > 1.645 or 5 + 1.645*[0.1/] = 5.041, when we know that the true population mean is given by μ = 5.15. Then the solution should proceed as follows: Since μ = 5.15, β = P(≤xc| μ = μ*) = P(≤5.041| μ*=5.15) = P([5.15 - 5.041]//[0.1/] = P(z≤1.05) and the power of the test is given by power = 1 – .0111 = .899. Is it true or false? Note that xc is thecritical value from the appropriate sampling distribution of the sample mean, μ is the population mean under null hypothesis, μ * is the true population mean, and x-bar is the sample mean. True False