Question

# A sample of 39 observations is selected from a normal population. The sample mean is 19,...

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

1. What is the decision rule?
• Reject H0 when z > 1.282

• Reject H0 when z ≤ 1.282

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

1. 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.)

a)

One-tailed test

b)

Reject H0 when z > 1.282

c)

 population mean μ= 18 sample mean 'x̄= 19 sample size    n= 39 std deviation σ= 4 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).

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