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 typically 7.4
(Reference: *Merck Manual*, a commonly used reference in
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 *x* = 6.9 with
sample standard deviation *s* = 2.7. Use a 10% level of
significance to test the claim that the drug has changed (either
way) the mean pH level of the blood.

(a) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

*H _{o}*:

(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 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 standard normal, since the sample size is large and
*σ* is known.

(c) Sketch the sampling distribution and show the area
corresponding to the *P*-value.

(d) Will you reject or fail to reject the null hypothesis? Are the
data statistically significant at level *α*?

At the *α* = 0.10 level, we fail to reject the null
hypothesis and conclude the data are not statistically
significant.At the *α* = 0.10 level, we reject the null
hypothesis and conclude the data are not statistically
significant. At the *α* = 0.10 level,
we reject the null hypothesis and conclude the data are
statistically significant.At the *α* = 0.10 level, we fail
to reject the null hypothesis and conclude the data are
statistically significant.

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

Fail to reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level.Fail to reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level. Reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level.Reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.

Answer #1

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...

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 = 8.5 with sample standard deviation s = 2.8.
Use a...

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 31 patients with arthritis took the
drug for 3 months. Blood tests showed that x = 8.5 with sample
standard deviation s = 2.5. Use a...

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 = 3.0.
Use a...

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 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...

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 = 3.3.
Use a...

Let x be a random variable representing dividend yield of bank
stocks. We may assume that x has a normal distribution with σ =
2.5%. A random sample of 10 bank stocks gave the following yields
(in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample
mean is x = 5.38%. Suppose that for the entire stock market, the
mean dividend yield is μ = 4.2%. Do these data indicate that the
dividend yield of all...

Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Then
x has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.
14
17
17
18
15
12
14
18
15
12
(i) Use a calculator with sample...

Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Then
x has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.
14
19
15
20
15
12
15
18
16
12
(i) Use a calculator with sample...

Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Then
x has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.
16
19
17
20
13
11
13
18
17
11
(i) Use a calculator with sample...

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