Question

You wish to test the following claim (Ha) at a significance level of α=0.005

      Ho:μ=72.7
      Ha:μ<72.7

You believe the population is normally distributed and you know the standard deviation is σ=12.6 You obtain a sample mean of M=69.7 for a sample of size n=59

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = _____________

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = _____________

The p-value is... (choose one)

• less than (or equal to) α
• greater than α

This test statistic leads to a decision to... (choose one)

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...(choose one)

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 72.7.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 72.7.
• The sample data support the claim that the population mean is less than 72.7.
• There is not sufficient sample evidence to support the claim that the population mean is less than 72.7.

Answer 1

Answer)

Ho : u = 72.7

Ha : u < 72.7

Given mean = 69.7

S.d = 12.6

n = 59

As the population standard deviation is known, we can use standard normal z test

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (69.7-72.7)/(12.6/√59)

Z = -1.83

From z table, p(z<-1.83) = 0.0336

P-value = 0.0336

P- value is greater than alpha (0.005)

As the obtained p-value is greater than alpha

We fail to reject the null hypothesish

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 72.7.