Question

Let *x* be a random variable representing
dividend yield of bank stocks. We may assume that *x* has a
normal distribution with σ = 2.0%. 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 = 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 = 4.9%; *H*_{1}:
μ > 4.9%; right-tailed*H*_{0}: μ = 4.9%;
*H*_{1}: μ < 4.9%;
left-tailed *H*_{0}: μ >
4.9%; *H*_{1}: μ = 4.9%;
right-tailed*H*_{0}: μ = 4.9%; *H*_{1}: μ
≠ 4.9%; two-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 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 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

a)

level of significance =0.01

*H*_{0}: μ = 4.9%; *H*_{1}: μ >
4.9%; right-tailed

b)

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

population mean μ= | 4.9 | |

sample mean 'x̄= | 5.380 | |

sample size n= | 10 | |

std deviation σ= | 2.000 | |

std error ='σx=σ/√n=2/√10= | 0.6325 | |

z statistic= ='(x̄-μ)/σx=(5.38-4.9)/0.632= |
0.76 |

c)

p value
= |
0.2236 |
(from excel:1*normsdist(-0.76) |

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 average yield for bank stocks is higher than that of the entire stock market.

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normal distribution with σ = 2.0%. A random sample of 10 bank
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