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* = 17.5, with sample standard deviation *s* = 4.6.
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* = 0.01.

(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 known.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.

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

(c) Find the *P*-value. (Round your answer to four decimal
places.)

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* = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.At the
*α* = 0.01 level, we reject the null hypothesis and conclude
the data are not statistically
significant. At the *α* = 0.01
level, we fail to reject the null hypothesis and conclude the data
are statistically significant.At the *α* = 0.01 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 0.01 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 0.01 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

Ans:

a)level of significance=0.01

H0: μ = 19.4; H1: μ ≠ 19.4

b)

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

Test statistic:

t=(17.5-19.4)/(4.6/SQRT(36))

t**=-2.478**

c)df=36-1=35

p-value=tdist(2.478,35,2)**=0.0182**

d)

At the *α* = 0.01 level, we **fail to reject the
null hypothesis** and conclude the data are **not
statistically significant.**

e)

There **is insufficient evidence** at the 0.01
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...

The price to earnings ratio (P/E) is an important tool in
financial work. A random sample of 14 large U.S. banks (J. P.
Morgan, Bank of America, and others) gave the following P/E
ratios.†
24
16
22
14
12
13
17
22
15
19
23
13
11
18
The sample mean is
x ≈ 17.1.
Generally speaking, a low P/E ratio indicates a "value" or
bargain stock. Suppose a recent copy of a magazine indicated that
the P/E ratio of...

Let x be a random variable representing dividend yield
of bank stocks. We may assume that x has a normal
distribution with σ = 2.8%. 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 = 4.7%.
Do these data indicate that the dividend yield of all...

Let x be a random variable representing dividend yield
of bank stocks. We may assume that x has a normal
distribution with σ = 3.2%. 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 = 4.5%.
Do these data indicate that the dividend yield of all...

Let x be a random variable representing
dividend yield of bank stocks. We may assume that x has a
normal distribution with σ = 2.0%. A random sample of 10 bank
stocks gave the following yields (in percents).
5.74.86.04.94.03.46.57.15.36.1
The sample mean is x = 5.38%. Suppose that for the entire stock
market, the mean dividend yield is μ = 4.9%. Do these data indicate
that the dividend yield of all bank stocks is higher than 4.9%? Use
α =...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 3 minutes ago

asked 11 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 19 minutes ago

asked 20 minutes ago

asked 20 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 32 minutes ago

asked 36 minutes ago