Check if answers and p values right and answer a,b,c You are hired by the mayor
ID: 3061691 • Letter: C
Question
Check if answers and p values right and answer a,b,c
You are hired by the mayor of California to study whether a
tax on liquor has decreased the share of California residents who report to
abuse of alcohol. You are able to obtain, for a sample of 9822 individuals,
information about their alcohol consumption habits.
N=9822
Abuse alcohol before tax a sample of 974
Abuse alcohol after tax a sample of 958
Null hypothesis: H0: Yi = 0 ; no changes in alcohol abuse
vs.
Alternative Hypothesis: Ha: Yi < 0 ; alcohol abuse decreased after tax adoption on alcohol in California
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.09835
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.00425
z = (p1 - p2) / SE
z = 0.38
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 0.38 or greater than 0.38.
Thus, the P-value = 0.704
A. What is your conclusion if you are testing at the 5% signicance level?
B. What is your conclusion if you are testing at the 1% signicance level?
C. What has been implicitly assumed in your analysis about the deter-
minants of liquor consumption in order to infer causality from the tax
change to liquor consumption?
Explanation / Answer
H0: p1 = p2
H0: p1 > p2
p1 = 974/9822 = 0.0992
p2 = 958/9822 = 0.0975
p = (p1 * n1 + p2 * n2)/(n1 + n2)
= (0.0992 * 9822 + 0.0975 * 9822)/(9822 + 9822)
= 0.09835
SE = sqrt(0.09835 * (1 - 0.09835) * (1/9822 + 1/9822))
= 0.00425
z = (p1 - p2)/SE
= (0.0992 - 0.0975)/0.00425
= 0.4
P-value = P(Z > 0.4)
= 1 - P(Z < 0.4)
= 1 - 0.6554
= 0.3446.
a) At 5% significance level as the p-value is greater than the significance level (0.3446 > 0.05), so the null hypothesis is not rejected.
b) At 1% significance level as the p-value is greater than the significance level (0.3446 > 0.01), so the null hypothesis is not rejected.
So there is not sufficient evidence to support the claim that alcohol abuse decreased after tax adaption on alcohol in california.