a) The standard deviations of both populations are known, so use the z statistic; the significance level is given as 0.05, as this is an one-tailed test, the rejection region of 0.05 lies in the right tail of the distribution (the > in the H1 hypothesis indicates right tail). As the significance level of 0.05 is found in the t-distribution table, look up the value of z under infinity degrees of freedom (if the significance level given in the problem is not found in the t-distribution table, then look up the value in the z table). b) Calculate z (use the formula 11-2 on page 313 in the text) c) Compare the z critical value and the z calculated value to take a decision regarding Ho
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- A data set includes data from student evaluations of courses. The summary statistics are nequals=8585, x overbarxequals=3.423.42, sequals=0.540.54. Use a 0.010.01 significance level to test the claim that the population of student course evaluations has a mean equal to 3.503.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.A study was done on body temperatures of men and women. 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 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? What is the test statistic, t? What is the P-value? State the conclusion for the test. b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.A professor wants to know whether or not there is a difference in comprehension of a lab assignment among students depending on if the instructions are given all in text, or if they are given primarily with visual illustrations. She randomly divides her class into two groups of 15, gives one group instructions in text and the second group instructions with visual illustrations. The following data summarizes the scores the students received on a test given after the lab. Let the populations be normally distributed with a population standard deviation of 5.32 points for both the text and visual illustrations. Text (Group 1) Visual Illustrations (Group 2) 57.3 59 45.3 57.6 87.1 72.9 61.2 83.2 43.1 64 87.3 76.7 75.2 78.2 88.2 64.4 67.5 89 86.2 72.9 67.2 88.2 54.4 43.8 93 97.1 89.2 95.1 52 84.1 Is there evidence to suggest that a difference exists in the comprehension of the lab based on the…
- Use the data and table below to test the indicated claim about the means of two populations. Assume that the two samples are independent simple randor samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Make sure you identify all values. An Exercise Science instructor at IVC was interested in comparing the resting pulse rates of students who exercise regularly and the pulse rates of those who de not exercise regularly. Independent simple random samples of 16 students who do not exercise regularly and 12 students who exercise regularly were selected and the resting pulse rates (in beats per minute) were recorded. The summary statistics are presented in the table below. Is there compelling statistical evidence that the mean resting pulse rate of people who do not exercise regularly is greater than the mean resting pulse rate of people who exercise regularly? Use a significance value of 0.05. Two-Sample T-Test Sample…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 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H1 H2 H₁₁₂ The test statistic, t, is (Round to two decimal places as needed.) OB. Ho: H₁₂ H₁: H₁In a random sample of males, it was found that 29 write with their left hands and 212 do not. In a random sample of females, it was found that 70 write with their left hands and 444 do not. Use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below.The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.4 mg, with a standard deviation of 3 mg. The mean tar content of a simple random sample of 25 filtered 100-mm cigarettes is 13.0 mg with a standard deviation of 3.8 mg. The accompanying table shows the data. 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. Let population 1 be unfiltered king-size cigarettes. Complete parts (a) through (c) below. Click the icon to view the data. a. Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have a mean tar content greater than that of filtered 100-mm cigarettes. What does the result suggest about the effectiveness of cigarette filters? Identify the null and alternative hypotheses. O B. Ho: H1 =H2 O C. Ho: H1 #H2 H1: H1 =H2 O A. Ho: H1 = H2 H:H1 H2 O F. Ho: H1 = H2 H1:H1> H2 H:H1=H2 Hq: H1…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. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: Hq ZH₂ OC. Ho: H₁ H₂ H₁: Hy > H₂ The test statistic, t, is. (Round to two decimal places as needed.) (Round to three decimal places as needed.) The P-value is State the conclusion for the test. C... OB. Ho: H₁ H₂ H₁: Hy #H₂ OD. Ho: Hg #U2 H₁: HyA 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 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho H1 H2 H₁: H1 H2 The test statistic, t, is -1.55. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) OB. Ho: H1 H2 H₁₁₂ D. Ho: H1 H2 H₁: H1 H2 Treatment Placebo μ H₁ H2 n 25 40 X 2.38 2.65 S 0.53 0.87A 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 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H¹/₂ H₁: H₁10Here is a link to a data set concerning treatment groups A and B. Before performing a t-test to determine if the two groups are different, researchers must first ascertain if the variance in the two groups is the same using an F test. Indicate whether the hypothesis below is the null or alternate hypothesis for the F test. The variance in group A is equal to the variance in group B Calculate the F statistic for this data set and report it in the box below, rounded to two decimal places. Use the formula =(1-(f.dist(F, df1,df2,true) in Excel to calculate the P value for the F statistic, and report it in the box below. Do not use the rounded value for F when calculating the P value. Use the value in the spreadsheet that has not been rounded. 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