Question

Socially conscious investors screen out stocks of alcohol and
tobacco makers, firms with poor environmental records, and
companies with poor labor practices. Some examples of "good,"
socially conscious companies are Johnson and Johnson, Dell
Computers, Bank of America, and Home Depot. The question is, are
such stocks overpriced? One measure of value is the P/E, or
price-to-earnings ratio. High P/E ratios may indicate a stock is
overpriced. For the S&P Stock Index of all major stocks, the
mean P/E ratio is *μ* = 19.4. A random sample of 36
"socially conscious" stocks gave a P/E ratio sample mean of
*x* = 17.9, with sample standard deviation *s* = 5.2.
Does this indicate that the mean P/E ratio of all socially
conscious stocks is different (either way) from the mean P/E ratio
of the S&P Stock Index? Use *α* = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *μ* = 19.4;
*H*_{1}: *μ* > 19.4

*H*_{0}: *μ* > 19.4;
*H*_{1}: *μ* = 19.4

*H*_{0}: *μ* = 19.4;
*H*_{1}: *μ* < 19.4

*H*_{0}: *μ* ≠ 19.4;
*H*_{1}: *μ* = 19.4

*H*_{0}: *μ* = 19.4;
*H*_{1}: *μ* ≠ 19.4

(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
*σ* is unknown

.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 known.

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

(c) Estimate the *P*-value.

*P*-value > 0.250

0.100 < *P*-value <
0.250

0.050 < *P*-value < 0.100

0.010 < *P*-value < 0.050

*P*-value < 0.010

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 *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 mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.There is insufficient evidence at the 0.05 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.

Answer #1

a) Level of significance a = 0.05

Null and alternative hypotheses

H0: μ = 19.4; H1: μ ≠ 19.4

b) sampling distribution we using is

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

Test statistic

t = (xbar - )/(s/√n)

t = (17.9 -19.4)/(5.2/√36)

t = -1.73

C) p-value for t = -1.73 , d.f = n-1 = 35 and two tailed test

p-value = 2* P( t < -1.73) d.f = 35

p-value = 0.0924

0.050 < p-value < 0.100

Here p-value = 0.0924 < 0.05

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

e) conclusion :

.There is insufficient evidence at the 0.05 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.

Socially conscious investors screen out stocks of alcohol and
tobacco makers, firms with poor environmental records, and
companies with poor labor practices. Some examples of "good,"
socially conscious companies are Johnson and Johnson, Dell
Computers, Bank of America, and Home Depot. The question is, are
such stocks overpriced? One measure of value is the P/E, or
price-to-earnings ratio. High P/E ratios may indicate a stock is
overpriced. For the S&P Stock Index of all major stocks, the
mean P/E ratio...

Socially conscious investors screen out stocks of alcohol and
tobacco makers, firms with poor environmental records, and
companies with poor labor practices. Some examples of "good,"
socially conscious companies are Johnson and Johnson, Dell
Computers, Bank of America, and Home Depot. The question is, are
such stocks overpriced? One measure of value is the P/E, or
price-to-earnings ratio. High P/E ratios may indicate a stock is
overpriced. For the S&P Stock Index of all major stocks, the
mean P/E ratio...

Socially conscious investors screen out stocks of alcohol and
tobacco makers, firms with poor environmental records, and
companies with poor labor practices. Some examples of "good,"
socially conscious companies are Johnson and Johnson, Dell
Computers, Bank of America, and Home Depot. The question is, are
such stocks overpriced? One measure of value is the P/E, or
price-to-earnings ratio. High P/E ratios may indicate a stock is
overpriced. For the S&P Stock Index of all major stocks, the
mean P/E ratio...

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 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 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 = 8.6 with sample
standard deviation s = 3.2. Use a...

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