Question

Question 5: 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 981 monitored subscribers, 289 of them opened the e-mail within 24 hours of receiving it. What is the 95% confidence interval for the true proportion of all e-mail subscribers that opened the e-mail within 24 hours of receiving it?

1)	( 0.67688 , 0.73393 )

2)	( 0.27066 , 0.31854 )

3)	( -0.26607 , 0.32312 )

4)	( 0.28004 , 0.30915 )

5)	( 0.26607 , 0.32312 )

Question 6: Based on past data, the producers of Ice Mountain bottled water knew that the proportion of people who preferred Ice Mountain to tap water was 0.691. To see how consumer perception of their product has changed, they decide to conduct a survey. Of the 84 respondents, 63 indicated that they preferred Ice Mountain to the tap water in their homes. The 90% confidence interval for this proportion is ( 0.6723 , 0.8277 ). What is the best conclusion of those listed below?

1)	The proportion of consumers who prefer Ice Mountain is 0.691 with 90% confidence.

2)	We can not claim that the proportion of consumers who prefer Ice Mountain to their tap water differs from 0.691.

3)	We can conclude that the proportion of consumers who prefer Ice Mountain to their tap water is larger than 0.691.

4)	The confidence interval does not provide enough information to form a conclusion.

5)	We can conclude that the proportion of consumers who prefer Ice Mountain to their tap water is smaller than 0.691.

Question 7: A restaurant wants to test a new in-store marketing scheme in a small number of stores before rolling it out nationwide. The new ad promotes a premium drink that they want to increase the sales of. 15 locations are chosen at random and the number of drinks sold are recorded for 2 months before the new ad campaign and 2 months after. The 95% confidence interval to estimate the true average difference in nationwide sales quantity before the ad campaign and after is (-36.7, -12.86). Which of the following is the appropriate conclusion? The differences were calculated as (after ad campaign- before ad campaign).

1)	We are 95% confident that the average difference in sales quantity for all stores is negative, with the higher sales coming after the ad campaign.

2)	We are 95% confident that the average difference in sales quantity for all stores is positive, with the higher sales coming after the ad campaign.

3)	There is not a significant difference between the average sales quantity before or after the ad campaign.

4)	We are 95% confident that the average difference in sales quantity for all stores is negative, with the higher sales being before the ad campaign.

5)	We are 95% confident that the average difference in sales quantity for all stores is positive, with the higher sales being before the ad campaign.

Answer 1

5. Given that x= 289 and sample size n = 981

Confidence level is 95 % hence Z crtical at 95 % confidence level is 1.96

as Confidence interval as

Where E= Margin of error calculated as

p=x/n = 0.2946

Hence E calculated as

0.015, Hence Confidence interval

5) (0.26607 to 0.32312)

Question no 6.

According to question the conclusion will be

1) The proportion of Consumer who prefer ice mountain is 0.691 Wuth 90 % confidence.

Question no 7.

According to ths question the conclusion will be

4). We are 95% confident that the average difference in sales quantity for all stores is negative, with the higher sales being before the ad campaign.