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 of36patients with arthritis took the drug for 3 months Blood tests showed that x 8 4with 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 (b) State the null and alternate hypotheses H 0 7 4 H 1 7 4 H 0 7 4 H 1 7 4 H 0 7 4 H 1 7 4 H 0 7 4 H 1 7 4 H 0 7 4 H 1 7 4 (c) 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 andis known The standard normal, since the sample size is large andis known The standard normal, since the sample size is large andis unknown The Student's t , since the sample size is large andis unknown What is the value of the sample test statistic (Round your answer to three decimal places ) (d)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 (e) Sketch the sampling distribution and show the area corresponding to the P value (f) 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 At the 0 05 level, we reject the null hypothesis and conclude the data are statistically significant At the 0 05 level, we reject the null hypothesis and conclude the data are not statistically significant At the 0 05 level, we fail to reject the null hypothesis and conclude the data are statistically significant At the 0 05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant (g) 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

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Sep 21, 2024

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

Letxbe a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of thexdistribution 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 of36patients with arthritis took the drug for 3 months. Blood tests showed thatx=8.4with sample standard deviations=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?

(b) 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

The Student'st, since the sample size is large andis known.
The standard normal, since the sample size is large andis known.
The standard normal, since the sample size is large andis unknown.
The Student'st, since the sample size is large andis unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)

(d)Estimate theP-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

(e) Sketch the sampling distribution and show the area corresponding to theP-value.

(f) 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?

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

(g) 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.