A simple random sample of 49 8th graders at a large suburban middle school indicated that 89% of them are involved with some type of after school...

A simple random sample of 49 8th graders at a large suburban middle school indicated that 89% of them are involved with some type of after school activity. Find the margin of error associated with a 95% confidence interval that estimates the proportion of them that are involved in an after school activity. 

a) 0.074

b) 0.088

c) 0.045

d) 0.274

e) 0.138

f) None of the above

Question 4

A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some type of after school activity. Find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. 

a) [0.719, 0.901]

b) [0.769, 0.774]

c) [0.639, 0.901]

d) [0.719, 0.701]

e) [0.619, 0.851]

f) None of the above

Question 5

Mars Inc. claims that they produce M&Ms with the following distributions:

 Brown  30%  Red  20%  Yellow  20%  Orange  10%  Green  10%  Blue  10% 

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

 Brown  24  Red  21  Yellow  21  Orange  15  Green  15  Blue  15 

Find the 99% confidence interval for the proportion of red M&Ms in that bag. 

a) [0.013, 0.285]

b) [0.093, 0.285]

c) [-0.007, 0.235]

d) [0.093, 0.085]

e) [0.143, 0.148]

f) None of the above

Question 6

Mars Inc. claims that they produce M&Ms with the following distributions:

 Brown  30%  Red  20%  Yellow  20%  Orange  10%  Green  10%  Blue  10% 

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

 Brown  22  Red  22  Yellow  22  Orange  12  Green  15  Blue  15 

Find the 95% confidence interval for the proportion of blue M&Ms in that bag. 

a) [0.074, 0.204]

b) [0.074, 0.004]

c) [0.124, 0.129]

d) [-0.026, 0.154]

e) [-0.006, 0.204]

f) None of the above

Question 7

Mars Inc. claims that they produce M&Ms with the following distributions:

 Brown  30%  Red  20%  Yellow  20%  Orange  10%  Green  10%  Blue  10% 

How many M&Ms must be sampled to construct the 97% confidence interval for the proportion of orange M&Ms in that bag if we want a margin of error of ± .15? 

a) 19

b) 18

c) 15

d) 14

e) 21

f) None of the above

Question 8

An experimenter flips a coin 100 times and gets 59 heads. Find the 98% confidence interval for the probability of flipping a head with this coin. 

a) [0.476, 0.704]

b) [0.376, 0.654]

c) [0.526, 0.531]

d) [0.476, 0.504]

e) [0.396, 0.704]

f) None of the above

Question 9

Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 89% confidence interval of width of at most .12 for the probability of flipping a head? 

a) 178

b) 104

c) 105

d) 177

e) 180

f) None of the above

Question 10

It has been observed that some persons who suffer acute heartburn are diagnosed with it again within one year of the first episode. This is due, in part, to damage from the first episode. In order to examine the percentage of the persons who suffer acute heartburn a second time, a random sample of 1100 people who suffered acute heartburn was collected. It was observed that 17 of them again suffered acute heartburn within one year. Select a 99% confidence interval for the true proportion of those who suffer a second episode. 

a) [0.00590, 0.0251]

b) [0.00690, 0.0551]

c) [0.0890, 0.0551]

d) [0.00690, 0.0351]

e) [0.00890, 0.0651]

f) None of the above

Question 11

When solving for the sample size required to estimate p to within a particular margin of error, under what circumstances do we use p̂ = .5?

a) When the margin of error desired is less than or equal to .5

b) When we have no prior information on the approximate value of p̂ or p.

c) When p̂ = .4 and 1 - p̂ = .6

d) When the computed value of p̂ = .5

e) When the variance is equal to .5 or when we desire a most conservative sample size.

f) None of the above

Question 12

Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 90% confident that their estimate will fall within 3% of the true population proportion? 

a) 741

b) 722

c) 703

d) 712

e) 729

f) None of the above

Question 13

An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 1% of the true proportion with 90% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy? 

a) 6748

b) 6775

c) 6754

d) 6766

e) 6785

f) None of the above

Question 14

It has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to two groups of people suffering a first episode are selected. There are 170 people in the first group and this group will be administered the new drug. There are 132 people in the second group and this group wil be administered a placebo. After one year, 14% of the first group has a second episode and 18% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups. 

a) [-0.044, 0.124]

b) [-0.124, 0.044]

c) [-0.110, 0.030]

d) [-0.030, -0.013]

e) [-0.610, 0.530]

f) None of the above