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 mu = 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 = 8.4 with sample standard deviation s = 2.9. 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: mu > 7.4; H1: mu = 7.4 H0: mu ≠ 7.4; H1: mu = 7.4 H0: mu = 7.4; H1: mu < 7.4 H0: mu = 7.4; H1: mu > 7.4 H0: mu = 7.4; H1: mu ≠ 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 unknown. The Student's t, since the sample size is large and o is unknown. 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 known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.150 0.100 < P-value < 0.150 0.050 < P-value < 0.100 0.020 < P-value < 0.050 P-value < 0.020 Sketch the sampling distribution and show the area corresponding to the P-value. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 as well as the area under the curve between 2.07 and 4 are both shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.07 and 4 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −2.07 and 4 is shaded. (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 a? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a = 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 mu = 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 = 8.4 with sample standard deviation s = 2.9. 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: mu > 7.4; H1: mu = 7.4 H0: mu ≠ 7.4; H1: mu = 7.4 H0: mu = 7.4; H1: mu < 7.4 H0: mu = 7.4; H1: mu > 7.4 H0: mu = 7.4; H1: mu ≠ 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 unknown. The Student's t, since the sample size is large and o is unknown. 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 known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.150 0.100 < P-value < 0.150 0.050 < P-value < 0.100 0.020 < P-value < 0.050 P-value < 0.020 Sketch the sampling distribution and show the area corresponding to the P-value. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 as well as the area under the curve between 2.07 and 4 are both shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.07 and 4 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 is shaded. A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −2.07 and 4 is shaded. (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 a? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a = 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀: mu > 7.4; H₁: mu = 7.4

H₀: mu ≠ 7.4; H₁: mu = 7.4

H₀: mu = 7.4; H₁: mu < 7.4

H₀: mu = 7.4; H₁: mu > 7.4

H₀: mu = 7.4; H₁: mu ≠ 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 unknown.

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

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 known.

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

(c)

Estimate the P-value.

P-value > 0.150

0.100 < P-value < 0.150

0.050 < P-value < 0.100

0.020 < P-value < 0.050

P-value < 0.020

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

A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −2.07 as well as the area under the curve between 2.07 and 4 are both shaded.

(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 a?

At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

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

At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the a = 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.

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