3. Null hypotheses for an independent-measures t test Which of the following null hypotheses is appropriate for an independent-measures t test? Ho: μ # 6 Ho: U1 = μ2 O Ho: μ = 0 Ho: μ1 μ2
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- The worldwide market share for a web browser was 20.1% in a recent month. Suppose that a sample of 200 random students at a certain university finds that 50 use the browser. At the 0.01 level of significance, is there evidence that the market share for the web browser at the university is greater than the worldwide market share of 20.1%? Determine the null and alternative hypotheses. A.H0: P≥0.201; H1: P<0.201 B.H0: P=0.201; H1: P≠0.201 C. H0: P≠0.201; H1: P=0.201 D. H0: P≤0.201; H1: P>0.201 ZStat=__ (Round to two decimal places) p-value=____ __A__ the null hypothesis. There is __B__ evidence to conclude that the market share at teh university is __C__ the worldwide market share of 20.1%. A: Reject or do not reject B: insufficient or sufficient C: at least, less than, equal to, at most, not equal to, greater thanA hypothesis test was conducted, at α = 0.05, to determine whether a certain chemical compound lasts longer than 30 seconds under a certain specified condition. The hypotheses used were: H0: µ = 30 Ha: µ > 30 A sample mean of 37.4 seconds was obtained from a sample of size n = 80. All statistical assumptions were met, and a p-value of p = 0.0089 was obtained. Which of the following is correct? a) If the null hypothesis were in reality true that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds from a sample of size n = 80 would be only .0089. b) If the null hypothesis were in reality false that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds (or less) from a sample of size n = 80 would be only .0089. c) If the null hypothesis were in reality true that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds (or greater) from…Let n1=40, X1=10, n2=40, and X2=20. Complete parts (a) and (b) below. a. At the 0.05 level of significance, is there evidence of a significant difference between the two population proportions? Determine the null and alternative hypotheses. Choose the correct answer below. A. H0: π1≤π2 H1: π1>π2 B. H0: π1≥π2 H1: π1<π2 C. H0: π1≠π2 H1: π1=π2 D. H0: π1=π2 H1: π1≠π2 Calculate the test statistic, ZSTAT, based on the difference p1−p2. The test statistic, ZSTAT, is ? (Type an integer or a decimal. Round to two decimal places as needed.) Calculate the p-value. The p-value is ? (Type an integer or a decimal. Round to three decimal places as needed.) b. Construct a 95% confidence interval estimate of the difference between the two population proportions. ?≤π1−π2≤? (Type integers or decimals. Round to four decimal places as needed.)
- The proportion of people that own cats is 20%. A veterinarian believes that this proportion is smaller than 20% and surveys 500 people. Test the veterinarian's claim at the α=0.05α=0.05 significance level. Preliminary: Is it safe to assume that n≤0.05n≤0.05 of all subjects in the population? Yes No Verify np(1−p)≥10.np(1-p)≥10. Round your answer to one decimal place.np(1−p)=np(1-p)= Test the claim: The null and alternative hypotheses are H0:μ=0.2Ha:μ≠0.2 H0:μ≥0.2Ha:μ<0.2 H0:p=0.2Ha:p<0.2 H0:μ≤0.2Ha:μ>0.2 H0:p=0.2Ha:p≠0.2 H0:p≤0.2Ha:p>0.2 The test isConsider the hypotheses shown below. Given that x overbarx=57, sigmaσ=12, n=35, alphaα=0.05, complete parts a and b. Upper H 0H0: muμ ≤55 Upper H 1H1: muμ>55 a. What conclusion should be drawn? The z-test statistic is The critical z-score(s) is(are) Because the test statistic the null hypothesis. b. Determine the p-value for this test. The p-value is(a) Find the P - value for the test statistic z=1.36 for the following null and alternative hypotheses:
- Match the p-values with the appropriate conclusion: I. 0.00001 II. 0.0189 III. 0.0611 IV. 0.4234(a) The evidence against the null hypothesis is significant, but only at the 10% level. (b) The evidence against the null and in favor of the alternative is very strong. (c) There is not enough evidence to reject the null hypothesis, even at the 10% level. (d) The result is significant at a 5% level but not at a 1% level.Conduct a test at the alphaαequals=0.05 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 p1>p2. The sample data are x1=120, n1=248, x2=133, and n2=302. (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 not equals p 2H1: p1≠p2 B. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 less than p 2H1: p1<p2 C. Upper H 0 : p 1 equals 0H0: p1=0 versus Upper H 1 : p 1 not equals 0H1: p1≠0 D. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 greater than p 2H1: p1>p2 Your answer is correct. (b) Determine the test statistic. z0equals=nothing (Round to two decimal places as needed.)A hypothesis test is performed in which the research (alternative) hypothesis states that more than 15% of a population are unemployed. The p-value for the test is calculated to be 0.018 (with the alpha = 0.05). Which of these statements is correct? A. We reject the null hypothesis and conclude that the research hypothesis is correct: more than 15% of the population are unemployed. B. We reject the null hypothesis and conclude that more than 18% of the population are unemployed. C. We fail to reject the null hypothesis and conclude that exactly 15% of the population are unemployed. D. We fail to reject the null hypothesis and conclude that exactly 85% of the population are unemployed.
- The proportion of people that own cats is 20%. A veterinarian believes that this proportion is larger than 20% and surveys 100 people. Test the veterinarian's claim at the a=0.025 significance level. Is it safe to assume that n ≤0.05 of all subjects in the population? No Yes Verify np(1-p)≥10. Round your answer to one decimal place.np(1-p)= The null and alternative hypotheses are Ho:p=0.2Ha:p<0.2 Ho:μ ≥0.2Ha:μ<0.2 Ho:p≤0.2Ha:p>0.2 Ho:μ≤0.2Ha:μ>0.2 Ho:p=0.2Ha:p≠0.2 Ho:μ=0.2Ha: μ ≠0.2 The test is a. right-tailed, b. two-tailed c. left-tailed Based on the sample of 100 people, 23% owned cats. Calculate the test statistic. Round to two decimal places.z = Calculate the p -value. Round to four decimal places. Make a decision. Fail to reject the null hypothesis Reject the null hypothesis Make a conclusion. There is sufficient evidence that the proportion of people who own cats is larger. There is not sufficient evidence that the proportion of people…Determine which of the following statements are true about the critical region. The critical region is a term used when the null hypothesis is rejected. The critical region is comprised of extreme sample values that are very unlikely to be obtained if the alternative hypothesis is true. The critical regions is determined by the alpha level. The critical region is comprised of extreme samples values that are very unlikely to be obtained if the null hypothesis is trueThe proportion of people that own cats is 70%. A veterinarian believes that this proportion is significantly different than 70% and surveys 700 people. Test the veterinarian's claim at the a=0.2 significance level. Is it safe to assume that n≤0.05 of all subjects in the population? No Yes Verify np(1-p)≥10. Round your answer to one decimal place.np(1-p)= The null and alternative hypotheses are Ho: p ≤ 0.7Ha:p >0.7 Ho:μ ≥0.7Ha: μ <0.7 Ho: μ ≤ 0.7Ha:μ > 0.7 Ho:p = 0.7Ha:p ≠ 0.7 Ho:μ = 0.7Ha:μ ≠ 0.7 Ho: p =0.7Ha :p<0.7 The test is a.right-tailed or b. two-tailed or c. left-tailed Based on the sample of 700 people, 79% workers were employed from networking. What is the test statistic? Round your answer to two decimal places. What is the p-value? Round your answer to four decimal places. Make a decision. Do not reject the null hypothesis. Reject the null hypothesis. Make a conclusion. There is sufficient evidence that the proportion of people…