dence. lestion 4: Hypothesis Testing: Each question is worth 7.5 marks Total (15

Question

dence. lestion 4: Hypothesis Testing: Each question is worth 7.5 marks Total (15 marks) A. Suppose that we know that the standard deviation of the population is 3ZWe have a sample size of 625W e also have a sample mean of 46.We also have a population mean of 43 Test the following hypothesis with a 0.01 43 H1: H 43 Yu B. A sample of 16 items produced a mean of 110 and the standard deviation of 25. Test the hypothesis that the population mean is less than 118 at 10% significance level. l morke ,Total (10

Explanation / Answer

As these are assignment questions, as per forum rules I am taking up 1 question (4th)

4. A.

Stdev of population = 3.7

n = 625

sample mean = 46

Pop. mean = 43

alpha = .01

Lets find the test statistic.

Z = (X-Mu)/(Sigma/sqrt(n)) = (46-43)/(3.7/sqrt(625)) = 20.2703

Since 2.575 ( critical value for alpha =.01), is less than Z statistic of 20.2703 we conclude that null hypothesis stands rejected. And therefore Mu!=43.

B.

n = 16

Mean = 110

Stdev = 25

alpha = .10, which means a critical Z value of -1.282

The hypothesis set is to :

Mu >= 118

Mu < 118

Z = (X-Mu)/Sigma = ( 110-118)/(25/sqrt(16)) = -1.28

Since our test statistic is in the critical zone (critical zone is Z<-1.28), we have to reject null hypothesis and accept the claim. So, in fact Mean is less than 118

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.