Question

You wish to test the following claim (HAHA) at a significance level of α=0.01α=0.01. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents pre-strike production and the second data set represents post-strike production.

      Ho:μd=0Ho:μd=0
      HA:μd<0HA:μd<0

You believe the population difference of production is normally distributed, but you do not know the standard deviation. You obtain pre-strike and post-strike production samples for n=6n=6 subjects. The average difference (post - pre) is ¯d=−47.4d¯=-47.4 with a standard deviation of the differences of sd=33.2sd=33.2.

Calculate the critical value accurate to the thousandths.
critical value =

Calculate the test statistic accurate to the thousandths.
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

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

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-strike from pre-strike production is less than 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-strike from pre-strike production is less than 0.
• The sample data support the claim that the mean difference of post-strike from pre-strike production is less than 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-strike from pre-strike production is less than 0.

Answer 1

Here we have d-47.4,s,-33.2, n -6 Hypotheses are α-0.01 Level of significance Test is one tailed (left tailed) Degree of freedom: df -n-1-5 Test Statistics: (-47.4-0)/(33.2/sqrt(6)) 7 -3.497 Critical value: CV3.365 Rejection Region: If t <-3.365, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value P-value-0.0087 Decision: Since p-value is less than level of significance so we reject the null hypothesis Excel function for critical value TINV(0.02,5) Excel function for p-value: -TDIST(3.497,5,1)

Conclusion:

• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-strike from pre-strike production is less than 0.