Let x be a random variable that represents the pH of arterial plasma (i.e., acid
ID: 2948800 • Letter: L
Question
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 = 8.3 with sample standard deviation s = 2.7. 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? 0.05 Correct: Your answer is correct. State the null and alternate hypotheses. 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 Correct: Your answer is correct. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, 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. The standard normal, since the sample size is large and ? is unknown. Correct: Your answer is correct. What is the value of the sample test statistic? (Round your answer to three decimal places.) 2.13 Incorrect: Your answer is incorrect. (c) Find the P-value. (Round your answer to four decimal places.)
Explanation / Answer
The statistical software output for this problem is:
One sample T summary hypothesis test:
? : Mean of population
H0 : ? = 7.4
HA : ? ? 7.4
Hypothesis test results:
Hence,
Test statistic = 2.134
P - value = 0.0390
Mean Sample Mean Std. Err. DF T-Stat P-value ? 8.3 0.42166916 40 2.1343747 0.039Related Questions
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