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 bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 5.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 5.0%? Use α = 0.01.

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

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

Answer 1

SOLUTION:

From given data,

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 bar = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 5.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 5.0%? Use α = 0.01.

5.7

4.8

6.0

4.9

4.0

3.4

6.5

7.1

5.3

6.1

Where,

= 5.38%

μ = 5.0%

σ = 2.8%

n = 10

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

the sample test statistic = z = ( -μ ) /(σ / sqrt(n))

z = (5.38 -5.0 ) /(2.8 / sqrt(10))

z = 0.38 / 0.885437

z = 0.42

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

As it is right tailed test P value is

P-value = P(z > 0.42) = 1 - P(z < 0.42) = 1-0.66276 = 0.3372

P-value = 0.3372