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 μ = 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 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.5 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) What is the level of significance?State the null and alternate hypotheses. H0: μ ≠ 7.4; H1: μ = 7.4 H0: μ > 7.4; H1: μ = 7.4 H0: μ = 7.4; H1: μ > 7.4 H0: μ = 7.4; H1: μ ≠ 7.4 H0: μ = 7.4; H1: μ < 7.4 (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 σ is known. The Student's t, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ 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-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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 μ = 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 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.5 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) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ ≠ 7.4; H₁: μ = 7.4

H₀: μ > 7.4; H₁: μ = 7.4

H₀: μ = 7.4; H₁: μ > 7.4

H₀: μ = 7.4; H₁: μ ≠ 7.4

H₀: μ = 7.4; H₁: μ < 7.4

(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 σ is known.

The Student's t, since the sample size is large and σ is unknown.

The standard normal, since the sample size is large and σ is known.

The standard normal, since the sample size is large and σ 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-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

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