(Solved by Humans)-Let x be a random variable representing dividend yield of bank

Question

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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???=?2.2%.?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???=?4.6%. Do these data indicate that the dividend yield of all bank stocks is higher than?4.6%? Use???=?0.01.
(a) What is the level of significance?
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State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀:???= 4.6%;?H₁:???> 4.6%; right-tailedH₀:???= 4.6%;?H₁:???< 4.6%; left-tailed????H₀:???= 4.6%;?H₁:?????4.6%; two-tailedH₀:???> 4.6%;?H₁:???= 4.6%; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's?t, since we assume that?x?has a normal distribution with known??.The Student's?t, since?n?is large with unknown??.????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??.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
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(c) Find (or estimate) the?P-value. (Round your answer to four decimal places.)
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