Question

# 8. A business wants to know whether two versions of an email offer have the same...

8. A business wants to know whether two versions of an email offer have the same click-through proportion. It sent a random sample of customers an email. It randomly decided which of the two offers went in each email. In the end, it had the following data. 706 out of the 1281 customers that received the first email, clicked on the offer. 614 out of the 1220 customers that received the second email, clicked on the offer.

(a) What is the sample proportion for group 1? (round to 5 digits after the decimal place)

(b) What is the sample proportion for group 2? (round to 5 digits after the decimal place)

(c) What is the difference in the sample proportions between groups 1 and 2? (round to 5 digits after the decimal place)

(d) What is the standard error for the difference in the sample proportions? (Use σp1−p2 and round to 5 digits after the decimal place.)

(e) What is the estimate of the left end of a 95% confidence interval? (Round to 5 digits after the decimal place.)

(f) What is the estimate of the right end of a 95% confidence interval? (Round to 5 digits after the decimal place.)

(g) Do we reject or not reject the null hypothesis that the population click-through proportions are the same at the .05 level of significance? Reject Not reject

(h) Can we interpret the difference in the population proportions as a causal effect? Yes, it has a causal interpretation. No, it does not have a causal interpretation.

a)

p1cap = X1/N1 = 706/1281 = 0.55113

b)

p1cap = X2/N2 = 614/1220 = 0.50328

c)

difference = 0.55113 - 0.50328 = 0.04785

d)

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.55113 * (1-0.55113)/1281 + 0.50328*(1-0.50328)/1220)
SE = 0.01995

e)

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.55113 - 0.50328 - 1.96*0.01995, 0.55113 - 0.50328 + 1.96*0.01995)
CI = (0.00875 , 0.08695)

left end = 0.00875

f)

right end = 0.08695

g)
Reject

h)

Yes, it has a causal interpretation

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• Researchers are interested in the relationship between binge drinking and membership in a Greek life organization...
• A food safety guideline is that the mercury in fish should be below 1 part per...
• The hedge-fund company Blackstone Group has selected 15 candidates for an interview. There are 120 applicants...
• PROBLEM #5: BINOMIAL DISTRIBUTION The firearms manufacturer that sells its firearms to the local sheriff’s department...
• 7. According to recent studies, about 68% of college students cheat. Suppose that 71% are accused...
• Two Sample Hypothesis Test Show all five steps in your analysis. To get full credit you...