Question

-14.44 points BBUnderStat10 8.1.019. 4. Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with a 2.7%. A random sa following yields (in percents). L'S 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 u than 4.0%? Use a= 0.01. 4.0%. Do these data indicate that the divic (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? Ho: 4%; H: H > 4%; right-tailed Ho: 4%; H: H 4%; two-tailed Họ: H> 4%; H: 4 = 4%; right-tailed Ho: H4%; H: H< 4%; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with known a. The standard normal, since we assume that x has a normal distribution with unknown a. The Student's t, since we assume that x has a normal distribution with known a. The Student'st, since n is large with unknown o. What is the value of the sample test statistic? (Round your answer to two decimal places.)

Answer 1

Here we have: x = 5.38 o = 2.7 n = 10 Level of significance: a = 0.01 Hypothesis: two tailed test. Ho, μ 4 Ha, u # 4 Correct option "A"

The standard normal since we assume x has a normal distribution with known 0. (o known) Test statistics: z-distribution 5.38-4 = 1.62 Z= 2.7 Vn V10 Critical value: Zcrit= Za2 = Zo.01/2 = ±2.576 Fail to eject the null hypothesis. Conclusion: Here we have not sufficient evidence to reject the null hypothesis. z-observed value is not greater or less than z-critical value.