Question

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 bank stocks
is higher than 4.7%? Use *α* = 0.01.

(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?

*H*_{0}: *μ* = 4.7%;
*H*_{1}: *μ* > 4.7%;
right-tailed*H*_{0}: *μ* > 4.7%;
*H*_{1}: *μ* = 4.7%;
right-tailed *H*_{0}:
*μ* = 4.7%; *H*_{1}: *μ*
< 4.7%; left-tailed*H*_{0}: *μ* = 4.7%;
*H*_{1}: *μ* ≠ 4.7%;
two-tailed

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

The standard normal, since we assume that *x* has a
normal distribution with known *σ*.The Student's *t*,
since *n* is large with unknown
*σ*. The Student's *t*,
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.)

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) State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.

Answer #1

Part a)

α = 0.01

To Test :-

H0 :- µ = 4.7

H1 :- µ > 4.7

Part b)

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

Test Statistic :-

Z = ( X - µ ) / ( σ / √(n))

Z = ( 5.38 - 4.7 ) / ( 2.8 / √( 10 ))

Z = 0.77

Part c)

P value = P ( Z < 0.768 ) = 0.2212

Part d)

Decision based on P value

Reject null hypothesis if P value < α = 0.01 level of
significance

Since 0.2212 > 0.01 ,hence we reject null hypothesis

**Result :- We fail to reject null
hypothesis**

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

part e)

There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.

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Let x be a random variable representing dividend yield
of bank stocks. We may assume that x has a normal
distribution with σ = 2.7%. 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...

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of bank stocks. We may assume that x has a normal
distribution with σ = 2.2%. A random sample of 10 bank
stocks gave the following yields (in percents).
5.7
4.8
6.0
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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...

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