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Let x be a random variable representing dividend yield of bank stocks. We may as

ID: 2922548 • Letter: L

Question

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with = 3.1%. A random sample of 10 bank stocks gave the following yields (in percents).

The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is = 4.6%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.6%? Use = 0.01.

(a) What is the level of significance?

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

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

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

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

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

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

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

5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 4.6
HA : > 4.6
Standard deviation = 3.1

Hypothesis test results:

Hence,

a) Level of significance = 0.01

b) The standard normal, since we assume that x has a normal distribution with known ; Option B

c) Sample test statistic = 0.80

d) P - value = 0.2131

Mean n Sample Mean Std. Err. Z-Stat P-value 10 5.38 0.98030607 0.79566986 0.2131