Assume that we have selected two independent random samples from populations hav
ID: 3374738 • Letter: A
Question
Assume that we have selected two independent random samples from populations having proportions p1 and p2 and that picture 1 = 800/1000 = 0.8 and picture 2 = 950/1000 = 0.95. Test H0: p1 – p2 > –.12 versus Ha: p1 – p2 < –.12 by using a p-value and by setting ? equal to .10, .05, .01, and .001. How much evidence is there that p2 exceeds p1 by more than .12? (Round p-value to 4 decimal and z value to 2 decimal places. Negative amount should be indicated by a minus sign.) what is the Z and P- value?
Explanation / Answer
First we summarize the data given to us as follows:
p1 = 0.8, n1 = 1000
p2 = 0.95, n2 = 1000
The hypotheses are as follows:
H0: p2 - p1 <= 0.12
Ha: p2 - p1 > 0.12
Now calculate the standard error using the formula:
S' = (p1*(1-p1)/n1 + p2*(1-p2)/n2)0.5 = (0.80*(1-0.80)/1000 + 0.95*(1-0.95)/1000)0.5 = 0.0144
Next we calculate the test statistic:
z = (p2-p1 - 0.12)/S' = ((0.95-0.80)-0.12)/0.0144 = 2.083
The p-value for this z-value is:
p = 0.0186
This is a right-tailed hypothesis test, hence we compare p with ?.
So,
When ? = 0.10, p < ?, so we reject the null hypothesis.
When ? = 0.05, p < ?, so we reject the null hypothesis.
When ? = 0.01, p > ?, so we cannot reject the null hypothesis.
When ? = 0.001, p > ?, so we cannot reject the null hypothesis.
This is the solution !!