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Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is u = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that X = 8.6 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. Ho: u * 7.4; H1: µ = 7.4 Ho: H = 7.4; H1: H < 7.4 Ho:μ> 74 Ημε 74 Hoμ 74 Ηνμε 74 Họ: H = 7.4; H: > 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.250 0.100 < P-valu .250 e < 0 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is u = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that X = 8.6 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. Ho: u * 7.4; H1: µ = 7.4 Ho: H = 7.4; H1: H < 7.4 Ho:μ> 74 Ημε 74 Hoμ 74 Ηνμε 74 Họ: H = 7.4; H: > 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.250 0.100 < P-valu .250 e < 0 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter19: Probability And Statistics In Engineering
Section: Chapter Questions
Problem 17P
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Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is u = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that X = 8.6 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. Ho: u * 7.4; H1: µ = 7.4 Ho: H = 7.4; H1: H < 7.4 Ho:μ> 74 Ημε 74 Hoμ 74 Ηνμε 74 Họ: H = 7.4; H: > 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.250 0.100 < P-valu .250 e < 0 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010
Transcribed Image Text:Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is u = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that X = 8.6 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. (a) What is the level of significance? State the null and alternate hypotheses. Ho: u * 7.4; H1: µ = 7.4 Ho: H = 7.4; H1: H < 7.4 Ho:μ> 74 Ημε 74 Hoμ 74 Ηνμε 74 Họ: H = 7.4; H: > 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.250 0.100 < P-valu .250 e < 0 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010
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