Question

A sample of 39 observations is selected from a normal population. The sample mean is 19, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.10 significance level.

H₀: μ ≤ 18

H₁: μ > 18

1. Is this a one- or two-tailed test?

• One-tailed test

• Two-tailed test

2. What is the decision rule?

• Reject H₀ when z > 1.282

• Reject H₀ when z ≤ 1.282

3. What is the value of the test statistic? (Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Fail to reject H₀

1. e-1. What is the p-value? (Round your answer to 4 decimal places.)

1. e-2. Interpret the p-value? (Round your final answer to 2 decimal places.)

Answer 1

a)

One-tailed test

b)

Reject H₀ when z > 1.282

c)

population mean μ=		18
sample mean 'x̄=		19.000
sample size    n=		39
std deviation σ=		4.00
std error ='σx=σ/√n=4/√39=		0.641
z test statistic= ='(x̄-μ)/σx=(19-18)/0.641=		1.56

d)

since test statistic falls in rejection region we reject null hypothesis

Reject H₀

e-1)

p value        =

0.0594

(from excel:1*normsdist(-1.56)

e-2_)

p value is probability of getting as or more extreme test statistic if null hypothesis is true(population mean is 18).

.