You work for the consumer insights department of a major big box retailer and yo

Question

You work for the consumer insights department of a major big box retailer and you are investigating the efficacy of a new e-mail marketing campaign. Through the use of e-mail analytics research, you have determined that in a sample of 990 monitored subscribers, 258 of them opened the e-mail within 24 hours of receiving it. What is the 90% confidence interval for the true proportion of all e-mail subscribers that opened the e-mail within 24 hours of receiving it?

Question 3 options:

1) ( -0.23766 , 0.28355 ) 2) ( 0.24665 , 0.27456 ) 3) ( 0.23766 , 0.28355 ) 4) ( 0.71645 , 0.76234 ) 5) ( 0.24273 , 0.27849 )

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.260606061          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.013951233          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.022947737          
lower bound = p^ - z(alpha/2) * sp =   0.237658324          
upper bound = p^ + z(alpha/2) * sp =    0.283553797          
              
Thus, the confidence interval is              
              
(   0.237658324   ,   0.283553797   ) [ANSWER, OPTION 3]

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.