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 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.1. 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 > 7.4H0: μ ≠ 7.4; H1: μ = 7.4 H0: μ > 7.4; H1: μ = 7.4H0: μ = 7.4; H1: μ ≠ 7.4H0: μ = 7.4; H1: μ < 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 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 unknown.The Student's t, since the sample size is large and σ is known. What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Estimate the P-value. P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood

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 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.1. 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 > 7.4H0: μ ≠ 7.4; H1: μ = 7.4 H0: μ > 7.4; H1: μ = 7.4H0: μ = 7.4; H1: μ ≠ 7.4H0: μ = 7.4; H1: μ < 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 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 unknown.The Student's t, since the sample size is large and σ is known. What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Estimate the P-value. P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ = 7.4; H₁: μ > 7.4H₀: μ ≠ 7.4; H₁: μ = 7.4 H₀: μ > 7.4; H₁: μ = 7.4H₀: μ = 7.4; H₁: μ ≠ 7.4H₀: μ = 7.4; H₁: μ < 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 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 unknown.The Student's t, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

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

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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