Question

My Notes -/20 polnts 2. BBBasicStat8Acc 9.1.019. Ask Your Teach 1.9 % . A random sample of 10 bank stocks gave the following yields (in percents) Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mcan is x 5.38%. Suppose that for the entire stock market, the mean dividend yicld is 4.7 %. Do these data indicate that the dividend yicld of all bank stocks is higher than 4.7 % ? Use a - 0.01 (a) What is the level of significancc? (Enter a number.) State the null and altermate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? HD A4.7%; H: 4.7% ; left - tailed Ho 4.7%; H:4.7 %; right-tailed - 4.7%; right - tailed Hoi 4.7%; ,: Hni 4.7 %; H, 4.7% ; two- tailed (b) What sampl ing distribution will you use? Explain the rationale for your cholce of sampl ing distribution The Student's t, since n is large with unknown o The standard normal, since we assumc that x has a normal distribution with unknown o The standard normal, since we assume that x has a normal distribution with known a The Student's t, since we assume that x has a normal distribution with known g. 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.) Skctch the sam pling distribution and show the arca corresponding to the P-value. (Sclect the correct graph.)

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test: : Mean of population Ho 4.7 HA 4.7 Standard deviation 1.9 Hypothesis test results: Mean n Sample Mean Std. Err P-value Z-Stat 10 5.38 0.60083276 1.1317625 0.1289

Hence,

a) Level of significance = 0.01

Hypotheses: Option C is correct.

b) Sampling distribution: Option C is correct.

Test statistic = 1.13

c) P - value = 0.1289