Question

A national tax authority randomly distributes tax returns to be audited to a pool of auditors. Last year’s average amount of extra taxes collected, due to audit, was £356 per audit. During her annual personnel review, Kristina was told that, based on a sample of 32 returns, the average amount of extra taxes collected on audits she performed was £372 with a standard deviation of 25. The personnel review board claimed that Kristina was too tough in assessing tax during an audit. The review board suggested tripling Kristina’s work load. Help Kristina share information with the review board as to whether the board’s claims are justified. Kristina wants to fully capture the truth as much as possible, so test at a 1% level of significance.

Answer 1

given data are:-

sample mean() = 372

sample size (n) = 32

sample sd(s) = 25

here, as the sample sd(s) is known we will do 1 sample t test for mean.

hypothesis:-

(this is the board's claim that Kristina was too tough in assessing tax during audit)

test statistic be:-

df= (n-1) = (32-1) = 31

the p value is :-

[ as this is a right tailed test ]

[ in any blank cell of excel type =T.DIST.RT(3.6204,31)]

decision:-

p value = 0.0005 < 0.01 (alpha)

we reject the null hypothesis and conclude that there is sufficient evidence to support the board's claim.