Letx be a random variable representing dividend yield of bank stocks. We may assume thatx has a normal distribution with σ = 3.3%. 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 = 4.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.0%? Use ? = 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%;H 1: μ > 4%; right-tailed H 0: μ > 4%;H 1: μ = 4%; right-tailed H 0: μ = 4%;H 1: μ H 0: μ = 4%;H 1: μ ≠ 4%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume thatx has a normal distribution with unknown σ.The Student'st, sincen is large with unknown σ. The standard normal, since we assume thatx has a normal distribution with known σ.The Student'st, since we assume thatx has a normal distribution with known σ. Compute thez value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.)

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 3.3%. A random sample of 10 bank stocks gave the following yields (in...

Letx be a random variable representing dividend yield of bank stocks. We may assume thatx has a normal distribution with σ = 3.3%. 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 = 4.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.0%? Use ? = 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%;H
₁: μ > 4%; right-tailed

H
₀: μ > 4%;H
₁: μ = 4%; right-tailed

H
₀: μ = 4%;H
₁: μ < 4%;="">

H
₀: μ = 4%;H
₁: μ ≠ 4%; two-tailed

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

The standard normal, since we assume thatx has a normal distribution with unknown σ.The Student'st, sincen is large with unknown σ. The standard normal, since we assume thatx has a normal distribution with known σ.The Student'st, since we assume thatx has a normal distribution with known σ.

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

(c) Find (or estimate) theP-value. (Round your answer to four decimal places.)

Jun 02, 2022

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Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 3.3%. A random sample of 10 bank stocks gave the following yields (in...

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