SOLUTION: Could adding a dash of pizzazz, like the promise of free pizza, turn our questionnaires into must-respond treasures? In our zany experiment, we mailed out 100 straightforward que

Algebra ->  Testmodule -> SOLUTION: Could adding a dash of pizzazz, like the promise of free pizza, turn our questionnaires into must-respond treasures? In our zany experiment, we mailed out 100 straightforward que      Log On


   

Question 1203708: Could adding a dash of pizzazz, like the promise of free pizza, turn our questionnaires
into must-respond treasures? In our zany experiment, we mailed out 100 straightforward questionnaires with no extra perks and got 65 responses. Then, we sent 98
questionnaires offering the tantalizing reward of a free pizza, and we received 78 replies.
Does this intriguing data suggest that adding incentives like free pizza might be the key
to turning our questionnaires into real page-turners (i.e., the proportion of responses
are more when offered free pizza)? Use α = 0.05
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you want to test whether adding a dish of pizzazz gets more replies or whether the sample differences are due to random variations in different samples.

no pizzazz gets 65 out of 100 responses.
pizzazz gets 78 out of 98 responses.

p1 = 65/100 = .65.
p2 = 78/98 = .7959183673.
p0 = (65 + 78) / (100 + 98) = 143/198 = .7222222222.
1 - p0 = .2777777777.

z-score formula is:
z = (p1 - p2) / s
s = standard error.

s = sqrt(p0 * (1-p0) * (1/n1 + 1/n2))
n1 is sample size of sample 1.
n2 is sample size of sample 2.
s becomes equal to sqrt(.7222222222 * .2777777777 * (1/100 + 1/98)) = .0636654379.

z = (p1 - p2) / s becomes z = (.65 - .7959183673) / .0636654379 which is equal to -2.291955764.

the area to the left of that z-score of -2.291955764 is equal to .0109540673.
that's your test alpha.
it is less than your critical alpha of .05.
that makes the results of the test significant, which means that the sample results are most likely not due to random variations in sample proportions, but an actual difference.
the conclusion is that the use of pizzazz does generate greater response rates.

i used an online calculator and got the same results.
here they are: