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Students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Assume that a simple random sample has been selected. Use a 0.05 signicance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute? 68 81 40 67 40 65 48 65 72 97 20 61 63 Q; 89 63 Perform the test assuming that the requirements are met. Identify the null and alternative hypotheses. Ho: 'V H1: V V (Type integers or decimals. Do not round.) Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. (Round to three decimal places as needed.) 7 the null hypothesis. There V sutticient evidence at the 0.05 significance level to a group the students are reasonably good at egmating one minute. State the conclusion about the null hypothesis, as well as the nal conclusion that addresses the original claim. Decide whether it appears that students are reasonably good at estimating one minute. V the claim that the times are from a population with a mean equal to 60 seconds: on this basis it that as Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 46 of the 52 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 98 of the 113 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis test? O A. HO: P1 = P2 O B. HO: P1 = P2 O C. Ho: P1 # P2 H1: P1 # P2 H1 : P1 P2 H1 : P1 # P2 Identify the test statistic. z= (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is the significance level of a = 0.05, so the null hypothesis. There V sufficient evidence to support the claim that echinacea treatment has an effect. b. Test the claim by constructing an appropriate confidence interval. The 95% confidence interval is