Question

Are biomedical engineering salaries in Miami equal to those in Minnesota or is there a difference? A study was conducted looking at 40 staff engineering salaries from Miami and 45 staff engineering salaries in Minnesota:

Miami – sample size =40, average salary = 69,000, sample standard deviation = 1250

Minnesota – sample size = 45, average salary = 72,000, sample standard deviation = 1450.

At a 0.05 level of significance, can we conclude there is a difference in salaries based on the random sampled data? (assume that the standard deviations from the population although unknown are equal)

Use the six steps of hypothesis testing to make your decision.

Answer 1

i am denoting the Miami group by sample 1 and Minnesota by sample 2.

given data are:-

the pooled standard deviation be:-

hypothesis:-

[ claim ]

here, we will do 2 sample t test for mean..assuming equal variance.

the test statistic be:-

df = () = (40+45-2) = 83

the p value is :-

[ in any blank cell of excel type =T.DIST(-10.1533,83,TRUE) ]

decision:-

p value = 0.0000 < 0.05 (Alpha)

we reject the null hypothesis.

conclusion:-

there is enough evidence to conclude that there is a difference in salaries based on the random sampled data.

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