Question

t x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.1%. 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 = 4.5%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.5%? Use α = 0.01.

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

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

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.86 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.50 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.50 grams? Use α = 0.10.

(c) Compute the z 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.)

Answer 1

The statistical software output for this problem is :

1)

z value = 1.33

P-value = 0.0926

2)

z value = -2.14

P-value = 0.0163