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

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) (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:

RELATED QUESTIONS
A well-known consulting firm wants to test how it can influence the proportion of... (answered by CPhill)

Free Careington We sell Google most trusted Plans. Our Plans are nubemr one ranked in... (answered by Fombitz)

i need help what is the formula to surface area... please this is worth like 1000 points... (answered by Alan3354)

I would appreciate your help on factoring these polynomials.could you show me how they... (answered by stanbon)

i have a 75% in my math class. we just took our exam. our exam is worth 15% of our... (answered by Alan3354)

The larger of the two numbers is 8 more than four times the smaller. If the larger is... (answered by edjones)

Can someone think of a logarithmic function that we encounter in our work or in our... (answered by stanbon)

Can someone think of an exponential function like compounding interest that we encounter... (answered by stanbon)

What is the mark up percentage of a hat that our cost is 4.95 our sell cost is... (answered by TimothyLamb)

Hello: I am currently dealing with a problem. We are suppose to set up a slot machine... (answered by oscargut)