Question

Suppose Wall Street securities firms paid out year-end bonuses of $125,500 per employee last year. We take a sample of employees at the ASBE securities firm to see whether the mean year-end bonus is greater than the reported mean of $125,500 for the population. You wish to test the following claim ( H a ) at a significance level of α = 0.005 . H o : μ = 125500 H a : μ > 125500 You believe the population is normally distributed and you know the standard deviation is σ = 2600 . You obtain a sample mean of ¯ x = 126332.7 for a sample of size n = 39 . What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.) The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 125500. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 125500. The sample data support the claim that the population mean is greater than 125500. There is not sufficient sample evidence to support the claim that the population mean is greater than 125500.

Answer 1

To test against

Here

sample mean

population standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a standard norma distribution.

We reject H₀ at 0.5% level of significance if P-value < 0.005

Now,

The value of the test statistic

P-value

Since P-value = 0.022746 > 0.005, so we fail to reject H₀ at 0.5% level of significance and we can conclude that there is not sufficient sample evidence to support the claim that the population mean is greater than 125500