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 bank stocks is higher
than 4.9%? 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?
H0: μ =
4.9%; H1: μ ≠ 4.9%;
two-tailedH0: μ >
4.9%; H1: μ = 4.9%;
right-tailed H0: μ =
4.9%; H1: μ < 4.9%;
left-tailedH0: μ =
4.9%; H1: μ > 4.9%;
right-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
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 known σ.The Student's t,
since n is large 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.