Question

What is the maximum acceptable average engine horsepower that can be produced based on Monday production data (8 engines were made and tested with average = 10 hp and standard deviation = 4.0)?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer maximum acceptable average engine horsepower on Monday______________

A check of the company records indicated that over the last week, 50 engines were made, with and average or 10.5 hp and standard deviation of 3. Given this new information, does the answer in question 1 change?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer significant difference (Monday sample average versus historical record): Yes________, No_________

Answer 1

Since we have to find the maximum acceptable average engine horsepower , we have to use t-test.

Given n = 8, average engine horsepower = 10 hp, standard deviation s = 4

confidence interval = t

CI = = ( 6.65, 13.34) =

The maximum acceptable average engine horsepower that can be produced based on Monday production data = 13.34 hp.

2) Yes answer in question one changes, because we can consider the given data as a population data with variance known and from that sample we took a small sample. Here we perform Z - test.

Confidence interval : =

CI = ( 7.92, 12.08)

For the new information, the maximum acceptable average engine horsepower that can be produced based on Monday production data = 12.08 hp.

Hypothesis

(Population mean and sample mean are equal)

(Population mean and sample mean are different)

test statistic Z = =

critical Z value for 0.05 level of significance = 1.96

|z| < critical value. Hence we fail to reject null hypothesis. There is no significant difference between Monday smple average and historical record.