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 = 7.4.1 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- 8.8 with sample standard deviation s - 3.3. 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 USE SALT (a) What is the level of significance? O State the null and alternate hypotheses. O Hạ: + 7.4; H,i-7.4 O Hại M = 7.4; H,: > 7.4 OHi - 7.4; H,: H< 7.4 O H;: > 7.4; H,: H- 7.4 OH: u- 7.4; H,:H7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. OP-value > 0.150 O 0.100 < P.value < 0.150 O 0.050 < P.value < 0.100 O 0.020 < P.value < 0.050 O P.value < 0.020 Sketch the sampling distribution and show the area corresponding to the P-value. -2 (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? O At the a- 0.0S level, we reject the null hypothesis and conclude the data are statistically significant.
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 = 7.4.1 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- 8.8 with sample standard deviation s - 3.3. 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 USE SALT (a) What is the level of significance? O State the null and alternate hypotheses. O Hạ: + 7.4; H,i-7.4 O Hại M = 7.4; H,: > 7.4 OHi - 7.4; H,: H< 7.4 O H;: > 7.4; H,: H- 7.4 OH: u- 7.4; H,:H7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. OP-value > 0.150 O 0.100 < P.value < 0.150 O 0.050 < P.value < 0.100 O 0.020 < P.value < 0.050 O P.value < 0.020 Sketch the sampling distribution and show the area corresponding to the P-value. -2 (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? O At the a- 0.0S level, we reject the null hypothesis and conclude the data are statistically significant.
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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Transcribed Image Text:Let x be a random variable that represents the pH of arterial plasma (l.e., acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4.t 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 = 8.8 with sample standard deviations = 3.3. 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 USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses.
O Hg: u + 7.4; H,: = 7.4
O Hg: H = 7.4; H,: H > 7.4
O H,: H = 7.4; H,i < 7.4
O Hi > 7.4; H,: H = 7.4
O H: = 7.4; H,: H# 7.4
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since the sample size is large
a is known.
O The standard normal, since the sample size is large and a is known.
O The standard normal, since the sample size is large and a is unknown.
O The Student's t, since the sample size is large and a is unknown.
What is the value of the sample test statistic? (Round your answer
three decimal places.)
(c) Estimate the P-value.
O P-value > 0.150
O 0.100 < P-value < 0.150
O 0.050 < P.-value < 0.100
O 0.020 < P-value < 0.050
O P-value < 0.020
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 a?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
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