Management of the Sycamore Steel Company wishes to determine if there is any difference in performance between the day and night shift workers. They randomly sample a group of 40 day-shift workers and found a mean output of 62 parts per hour with a standard deviation of 9 parts per hour. A random sample of 30 night shift workers found an output of 67 parts per hour and a standard deviation of 8 parts per hour. At the 0.05 level of significance is there a difference between the day and night shift works?

Question

anonymous · Answer

@satellite73

dumbcow · Answer

you weren't able to get the answer ?

anonymous · Answer

The equation you provided was the wrong equation sorry.  :-(

dumbcow · Answer

oh im sorry, i assumed this is comparing 2 sample means

anonymous · Answer

It is but the means are different.

anonymous · Answer

Sorry your formula was correct after all I'm used to very different notation that's all.  :-)

dumbcow · Answer

oh ok , i was going to say it does also depend on whether the population variance is equal or not
i think you should assume equal variance here

anonymous · Answer

So, here's what I have so far, Sp=sqrt(73.75)
T=1.6676

anonymous · Answer

@dumbcow

dumbcow · Answer

yes thats what i get for Sp but i get a different test statistic $$T = \frac{67-62}{S_p \sqrt{\frac{1}{40} + \frac{1}{30}}} = \frac{5}{\sqrt{73.75} \sqrt{\frac{7}{120}}} = 2.41$$ critical value for df =68, alpha = .05 is about 2 http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf Therefore you would reject null hypothesis and conclude there is significant difference in performance between day and night shifts @rosho