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. |
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 H_{0}
Answer : Zdata = −15.81, Zcrit = -1.645, reject H0.
Option d. is correct.
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