The key numerical inputs in a sample size calculation are: Select all that apply: Group of answer choices The expected variability of the endpoint being measured Probability of a type I error (α) The number π Probability of a type II error (β) (Or, equivalently, the desired statistical power of the hypothesis test, 1–β) The correlation of α and β The size of treatment effect that we wish to detect (Delta or Δ or δ)
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- Test the claim about the difference between two population means u, and u, at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. Claim: µ, =H2; a = 0.01 Population statistics: o, = 3.4, o2 =1.7 Sample statistics: X, = 15, n, = 27, X2 = 17, n2 = 30 Determine the alternative hypothesis. Ha: H1 H2 Determine the standardized test statistic. (Round to two decimal places as needed.) Determine the P-value. P-value = (Round to three decimal places as needed.) What is the proper decision? Enil to rninat U Thore ie not onounh cidencoot the 0L Inunl of eianiinonon tn minnt the olainn Click to select your answer(s). 2:24PMPopulation 2 Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether u, > Hz at the a = 0.01 level of significance for the given sample data. (b) Construct a 95% confidence interval about u1 - H2. Population 1 29 23 45.6 42.9 4.1 11.8 O A. Ho: H1 = #2 H1: H1 # H2 YB. Ho: H1 = H2 H: H1> H2 O C. Ho: H1>H2 H: H1 =H2 O D. Ho: H1 H2. B. Do not reject Ho. There is not sufficient evidence at the a = 0.01 level of significance to conclude that u, > u2. O C. Reject Ho. There is sufficient evidence at the a = 0.01 level of significance to conclude that u, >H2. O D. Reject Ho. There is not sufficient evidence at the a = 0.01 level of significance to conclude that u1 > H2. (b) The 95% confidence interval about u, - uz is the range from a lower bound of to an upper bound of (Round to three decimal places as needed.)Treatment Placebo A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts. H1 H2 In 34 31 2.39 2.68 S 0.62 0.98 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O B. Ho: H1 H2 OC. Ho: H1 =H2 O D. Ho: H1 H2 H1: H1Statistics students in Oxnard College sampled 11 textbooks in the Condor bookstore, and recorded number of pages in each textbook and its cost. The bivariate data is shown below, Number of Pages (xx) Cost(yy) 695 104.4 481 75.72 329 62.48 427 67.24 743 110.16 509 76.08 641 104.92 921 123.52 466 82.92 944 124.28 529 85.48 A student calculates a linear modelyy = xx + . (Please show your answers to two decimal places)Use the model above to estimate the cost when number of pages is 285Cost = $ (Please show your answer to 2 decimal places.)Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the mean score is higher. She samples 10 statistics students and obtains the scores: Grades 73.5 88 63.9 85.5 62.7 65 83.2 61.9 88 62.7 Test grades are believed to be normally distributed.Use a significance level of 5%. State the alternative hypothesis: HA:HA: μ>65μ>65 μ<65μ<65 μ≠65μ≠65 State the mean of the sample: State the standard error of the sample means: State the test statistic: t=t= State the p-value: Decision: Fail to reject the null hypothesis. Reject the null hypothesis.Treatment Placebo A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. H1 H2 n 26 34 2.32 2.66 0.61 0.99 "TPL P2 OC. Ho: H1 H2 The test statistic, t, is -1.64. (Round to two decimal places as needed.) The P-value is 0.107. (Round to three decimal places as needed.) State the conclusion for the test. A. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. B. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. C. Fail to reject the null hypothesis. There is not sufficient evidence…Considering that the dependent variable (DV) is categorical, what ANOVA procedure would you like to use if there is a single between-subject IV with two groups? Group of answer choices One-Way ANOVA Two-way ANOVA Split-Plot ANOVA Repeated Measures ANOVA None of the AboveTest the claim that the proportion of people who own cats is smaller than 70% at the 0.1 significance level.The alternative hypothesis would be: p<0.7p<0.7 p≠0.7p≠0.7 μ>0.7μ>0.7 μ<0.7μ<0.7 μ≠0.7μ≠0.7 p>0.7p>0.7 The test is: left-tailed right-tailed two-tailed Based on a sample of 600 people, 66% owned catsThe test statistic is: (to 2 decimals)The p-value is: (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesisTreatment Placebo A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. H1 H2 In 30 34 X 2.34 2.65 0.89 0.6217. Question content area top Part 1 Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ=52,400; α=0.10 Sample statistics: x=53,647, s=3000, n=20 LOADING... Click the icon to view the t-distribution table. Question content area bottom Part 1 What are the null and alternative hypotheses? Choose the correct answer below. A. H0: μ≠52,400 Ha: μ=52,400 B. H0: μ≥52,400 Ha: μ<52,400 C. H0: μ=52,400 Ha: μ≠52,400 D. H0: μ≤52,400 Ha: μ>52,400 Part 2 What is the value of the standardized test statistic? The standardized test statistic is enter your response here . (Round to two decimal places as needed.) Part 3 What is(are) the critical value(s)? The critical value(s) is(are) enter your response here . (Round to three decimal places as needed. Use…Drug Trial ProblemClinical trials for a drug was conducted using a treatment group and a placebo group. The results are shown in the table below. Treatment Placebo μ μ₁ μ₂ n 33 38 x̄ 2.31 2.87 s 0.85 0.71 Use a 0.05 significance level to test the claim that the two samples are from populations with different means. State the claim, null, and alternative hypothesis. Claim: μ1 μ2 HO: μ1 μ2 H1: μ1 μ2