Question

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 a certain stock index is μ = 18. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and σ = 5.3. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.05.

(a) What is the level of significance?

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

H0: μ ≠ 18; H1: μ = 18; two-tailed

H0: μ = 18; H1: μ > 18; right-tailed

H0: μ = 18; H1: μ ≠ 18; two-tailed

H0: μ = 18; H1: μ < 18; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution with known σ.

The Student's t, since n is large with unknown σ.

The standard normal, since we assume that x has a normal distribution with known σ.

The standard normal, since we assume that x has a normal distribution with unknown σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

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

Answer #1

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...

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...

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 = 3.3%. 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 = 4.8%.
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 =
2.5%. 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 representing dividend yield of bank
stocks. We may assume that x has a normal distribution with σ =
2.3%. 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 = 4.4%.
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 =
2.5%. 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 = 4.6%. 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 = 2.3%. 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 = 4.9%.
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).
5.7
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 = 4.6%.
Do these data indicate that the dividend yield of all...

Nationally, about 11% of the total U.S. wheat crop is destroyed
each year by hail.† An insurance company is studying wheat hail
damage claims in a county in Colorado. A random sample of 16 claims
in the county reported the percentage of their wheat lost to hail.
13 6 10 13 12 20 16 9 7 8 25 18 15 9 14 6
The sample mean is x = 12.6%. Let x be a random variable that
represents the percentage...

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