Let x be a random variable representing dividend yield o bank stocks. we may ass

Question

Let x be a random variable representing dividend yield o bank stocks. we may assume that x has a normal distribution with ·2.8% A random sample of 10 bank stocks gove the following yieids (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 far the entire stock market the mean dividend yield is -46%. Do these data indicate that the dividend yield of all bank stocks is higher than46%? Use a =001. (a) What Is the level of significance? State the null and alternate hypotheses, will you use a left-tailed, rnight-talled, or two-tailed test? Ho: = 4.6%; H1 : +4.6%; two-tailed " Ho: -4.6%; H1: > 46%; right-tailed MO: > 4.0%; H1 : -4.0%; right-tailed H 0: -4.6%; H1 :

Explanation / Answer

question 1

using minitab

Test of = 4.6 vs < 4.6
The assumed standard deviation = 2.8

Variable N Mean StDev SE Mean 99% Upper Bound Z P
x 10 5.380 1.136 0.885 7.440 0.88 0.8106

question 2)

  

One-Sample Z: x

Test of = 85 vs > 85
The assumed standard deviation = 12.5

Variable N Mean StDev SE Mean 95% Lower Bound Z P
x 8 93.13 9.52 4.42 85.86 1.84 0.0329

question 3)

  

Test of = 4.5 vs < 4.5
The assumed standard deviation = 0.76

Variable N Mean StDev SE Mean 90% Upper Bound Z P
x 6 3.750 0.701 0.310 4.148 -2.42 0.0078

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