Let x be a random variable representing dividend yield of bank stocks. We may as
ID: 3309870 • 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 = 2.7%. 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 = 4.5%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.5%? Use = 0.01. (a) What is the level of significance? 0.01 Correct: Your answer is correct. State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: > 4.5%; H1: = 4.5%; right-tailed H0: = 4.5%; H1: 4.5%; two-tailed H0: = 4.5%; H1: > 4.5%; right-tailed H0: = 4.5%; H1: < 4.5%; left-tailed Correct: Your answer is correct. (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 Student's t, 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 standard normal, since we assume that x has a normal distribution with known . Correct: Your answer is correct. What is the value of the sample test statistic? (Round your answer to two decimal places.) 1.04 Incorrect: Your answer is incorrect. (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Incorrect with credit: Your answer is incorrect, but you received credit for a previous answer. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. Correct: Your answer is correct. (e) State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. Correct: Your answer is correct.
Explanation / Answer
The statistical software output for this problem is:
One sample Z summary hypothesis test:
: Mean of population
H0 : = 4.5
HA : > 4.5
Standard deviation = 2.7
Hypothesis test results:
Hence,
Test statistic = 1.03
P - value = 0.1513
Mean n Sample Mean Std. Err. Z-Stat P-value 10 5.38 0.85381497 1.0306683 0.1513Related Questions
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