Question

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 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.2. 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 unknown.

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

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

(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.

Answer #1

a)

0.05 is level of significance

H0: μ = 7.4; H1: μ ≠ 7.4

b)

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

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (8.6 - 7.4)/(3.2/sqrt(41))

t = 2.401

c)

P-value = 0.0211

0.010 < P-value < 0.050

d)

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

e)

There is sufficient 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
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arterial plasma (i.e., acidity of the blood). For healthy adults,
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drug for 3 months. Blood tests showed that x = 8.6 with sample
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arterial plasma (i.e., acidity of the blood). For healthy adults,
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drug for arthritis has been developed. However, it is thought that
this drug may change blood pH. A random sample of 36 patients with
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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 =
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arterial plasma (i.e., acidity of the blood). For healthy adults,
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medical schools and nursing programs). A new drug for arthritis has
been developed. However, it is thought that this drug may change
blood pH. A random sample of 33 patients with arthritis took the
drug for 3 months. Blood tests showed that...

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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 of 41 patients with
arthritis took the drug for 3 months. Blood tests showed that
x = 8.6 with sample standard deviation s = 3.4.
Use a...

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plasma (i.e., acidity of the blood). For healthy adults, the mean
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