Question

A national survey by BIGresearch in 2009 said that men on average spend $102.50 for Valentine’s Day. A study involving 40 men revealed that on average these men spent $90 for Valentine’s Day in 2010. Assume that σ = $5 and normally distributed population. Use a hypothesis test to determine if Valentine’s Day spending has decreased from 2009 to 2010, using α = 0.05.

a.	Zdata = 15.81, Zcrit = -1.96, reject H0.
b.	Zdata = −26.32, Zcrit = 2.57, reject H0.
c.	Zdata = −26.32 , Zcrit = 1.645, reject H0.
d.	Zdata = −15.81, Zcrit = -1.645, reject H0.

Answer 1

Solution:

Claim :  if Valentine’s Day spending has decreased

Left tailed test

Now ,

Zdata =   = 90 - 102.50]/[5/40] = -15.51

For left tailed test , critical value is

Rejection region: < -1.645

Here , -15.51 < -1.645

So , reject H₀

Answer : Zdata = −15.81, Zcrit = -1.645, reject H0.  

Option d. is correct.