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 less 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 = 0.05 .
H o : μ = 125500
H a : μ < 125500

You believe the population is normally distributed and you know the standard deviation is σ = 2900 . You obtain a sample mean of ¯ x = 124505.7 for a sample of size n = 49 .

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) αα
• greater than αα

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 less than 125500.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 125500.
• The sample data support the claim that the population mean is less than 125500.
• There is not sufficient sample evidence to support the claim that the population mean is less than 125500.

Answer 1

Z test hypothesis.

Given tht Nutl hyathe sis H Altevnctive the 8is Iti) : l125S00 2 Sgmsi cance devel O.C5 Sample Sae n) = 49 , Gample mecan (J 124S05.7 Standard deuiation (a 00 1 14 Test statetic (z) 124505-7- 125500) L-statistic Z- Statistic -2.4000 |stut 2.4c00 P-Value 0.5 Plocz-2.4) 1 -24 tevel Snificance Reect Null othesis leSs than is PVealue (Pe) Evident rejection e oaxven to Sufficient Poftulation mec«n ls tfan 25500 clain hat the