In a randomized doubleblind, placebo-controlled trial of children, an herb was tested as a treatment for upper respiratory infections in children. "Days of fever\" was one criterion used to measure effects. Among 305 children treated with the herb, the mean number of days with fever was 0.94, with a standard deviation of 1.46 days. Among 395 children given a placebo, the mean number of days with fever was 0.78 with a standard deviation of 1.08 days. Use a 0.05 signicance level to test the claim that the herb affects the number of days with fever. Based on these results, does the herb appear to be effective? 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 children treated with the herb. Identify the null and alternative hypotheses. H05 \"1 #112 H05P1P2 V H05P1=P2 H05P1=P2 H05 \"1 >112 H15P1P2 H15P1112 H15P1P2 H15P1=P2 The test statistic is - 3.30 . (Round to two decimal places as needed.) The Pvalue is :|. (Round to three decimal places as needed.) Treatment Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. 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. a. Use a 0.05 signicance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? H0:p1#p2 H01p1P2 The test statistic, t, is 0.53 . (Round to two decimal places as needed.) The P-value is . (Round to three decimal places as needed.) A person's body mass index (BMI) is computed by dividing the weight (kg) by the square of height (m). The accompanying table contains the BMI statistics for random samples of males and females. 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 females. Complete parts (a) through (c) below. @ Click the icon to view the table of statistics. a. Use a 0.05 signicance level to test the claim that females and males have the same mean BMI. Identify the null and alternative hypotheses. H02 H1 *Pz \"03141:\"2 V H05P1=P2 H13P1=P2 H15P1P2 H0411 =P2 H13P1=P2 H13P1=P2 H13P1>P2 The test statistic is . (Round to two decimal places as needed.) Statistics Female BMI: Male BMI: Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Treat the values as simple random samples from larger populations. Complete parts (a) and (b) below. All measurements are in years. @ Click the icon to view the table of longevities of archbishops and monarchs. a. Use a 0.05 signicance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs. Hoill15l12 Hoill1l12 H15P1>P2 H15P1>P2 V H05P1=P2 H05P1=P2 H15P1