Question

****PLEASE ANSWER ALL OF FOUR QUESTIONS!!!!****

QUESTION 1: You are curious about the average number of yards Matthew Stafford throws for each game for the Detroit Lions. You randomly select 30 games and see that the average yards per game is 269.1 with a standard deviation of 27.31 yards. You want to create a 90% confidence interval for the true average number of yards per game he throws. What is the margin of error for this estimate?

QUESTION 2: 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 825 monitored subscribers, 105 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: The Student Recreation Center wanted to determine what sort of physical activity was preferred by students. In a survey of 88 students, 56 indicated that they preferred outdoor exercise over exercising in a gym. The 90% confidence interval estimating the proportion of all students at the university who prefer outdoor exercise is given by which of the following?

QUESTION 4: Based on past data, the proportion of Major League Baseball (MLB) players who bat left handed was 0.344. You are interested to see if this is still the case. You conduct a sample of 49 players and find that 22 are left handed hitters. The 95% confidence interval is ( 0.3097 , 0.5882 ). What is the best conclusion of those listed below?

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

2)	We can not claim that the proportion of MLB players who are left handed hitters differs from 0.344.

3)	We can claim that the proportion of MLB players who are left handed hitters is smaller than 0.344.

4)	The proportion of MLB players who used to be left handed from 0.344 is 95%.

5)	We can claim that the proportion of MLB players who are left handed hitters is larger than 0.344.

Answer 1

QUESTION 1:

n=30

s =27.31

90 % confidence interval

Formula

tc =1.699 ( using t-table )

90 % confidence interval is

QUESTION 2:

n=88

x=56

90% confidence interval for proportion

Formula

Zc= 1.645 ( using z-table )

90 % confidence interval for proportion is