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 ? = 7.4.† 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 = 8.4 with sample standard deviation s = 2.5. 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) State the null and alternate hypotheses. choose one: H0: ? = 7.4; H1: ? ≠ 7.4 H0: ? = 7.4; H1: ? > 7.4 H0: ? > 7.4; H1: ? = 7.4 H0: ? = 7.4; H1: ? < 7.4 H0: ? ≠ 7.4; H1: ? = 7.4 b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. choose one: The Student's t, since the sample size is large and ? is unknown. The standard normal, since the sample size is large and ? is unknown. The Student's t, since the sample size is large and ? is known. The standard normal, since the sample size is large and ? is known. c) What is the value of the sample test statistic? (Round your answer to three decimal places.)
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 ? = 7.4.† 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 = 8.4 with sample standard deviation s = 2.5. 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) State the null and alternate hypotheses. choose one:
H0: ? = 7.4; H1: ? ≠ 7.4
H0: ? = 7.4; H1: ? > 7.4
H0: ? > 7.4; H1: ? = 7.4
H0: ? = 7.4; H1: ? < 7.4
H0: ? ≠ 7.4; H1: ? = 7.4
b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. choose one:
The Student's t, since the
The standard normal, since the sample size is large and ? is unknown.
The Student's t, since the sample size is large and ? is known.
The standard normal, since the sample size is large and ? is known.
c) What is the value of the sample test statistic? (Round your answer to three decimal places.)
Given:
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