An audit firm thinks that the average annual salary of a senior level accountant

Question

An audit firm thinks that the average annual salary of a senior level accountant at a construction company exceeds $82,000. A random sample of 20 accountants in similar roles reveals an average salary of $89,600 with a sample standard deviation of $12,700. Assume the salaries of the managers are normally distributed. (alpha = 0.05)  

1) State the Null Hypothesis:
2)State the Alternate:
3)State the significance level & one or two tailed:
4)State the statistic:
State the Decision Rule
5)Perform the Calculation – Make the decision.
6)Interpret the result:

Explanation / Answer

1) null hypothesis: mean <=82000

2)alternate hpothesis: mean >82000

3) significance level :0.05 ; one tailed(right tailed)

4) test statisitic:t; as we do not know population std deviation

decision rule: at 0.05 level and (n-1=19) degree of fredom rejection region: t>1.729

5) std error of mean=std deviation/(n)1/2 =2839.806

hence test stat t=(X-mean)/std error =(89600-82000)/2389.806=2.676

as test stat is in rejection region ; we reject null hypothesis

6) we have sufficient evidence to conclude that mean annual salary of a senior level accountant at a construction company exceeds $82,000.

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