Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.9%. 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 = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.1%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.1%? Use α = 0.01. (a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 4.1%; H1: μ > 4.1%; right-tailedH0: μ = 4.1%; H1: μ < 4.1%; left-tailed H0: μ > 4.1%; H1: μ = 4.1%; right-tailedH0: μ = 4.1%; H1: μ ≠ 4.1%; two-tailed (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 σ.The standard normal, since we assume that x has a normal distribution with unknown σ. 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. Compute the z value of the sample test statistic. (Enter a number. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(a)

What is the level of significance? (Enter a number.)

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ = 4.1%; H₁: μ > 4.1%; right-tailedH₀: μ = 4.1%; H₁: μ < 4.1%; left-tailed H₀: μ > 4.1%; H₁: μ = 4.1%; right-tailedH₀: μ = 4.1%; H₁: μ ≠ 4.1%; two-tailed

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

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

(c)

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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