1. Are you getting more spam in your personal email account? Suppose that 60% of adult email users would say "Yes." A polling firm contacts an SRS of 1000 people chosen from this population. If the sample were repeated many times, what would be the range of sample proportions who say "Yes," according to the 95 part of the 68-95-99.7 rule?

Range: 

 

 

2. Over half of all American teens (ages 12 to 17 years) have an online profile, mainly on Facebook. A random sample of 464 teens with profiles found that 342 included photos of themselves.

(a) Give the 90% large-sample confidence interval for the proportion p of all teens with profiles who include photos of themselves. 

Large-sample Interval: 

 

(b) Give the plus four 90% confidence interval for p . (The plus-four interval always pulls the results away from 0% or 100%, whichever is closer. Even though the condition for using the large-sample interval is met, the plus four interval is more trustworthy.) 

Plus four Interval:

 

 

3. A Gallup poll asked a sample of Canadian adults if they thought the law should allow doctors to end the life of a patient who is in great pain and near death if the patient makes a request in writing. The poll included 280 people in Quebec, 199 of whom agreed that doctor-assisted suicide should be allowed.

(a) What is the margin of error of the large-sample 96% confidence interval for the proportion of all Quebec adults who would allow doctor-assisted suicide? 

MoE: 

 

(b) How large a sample is needed to get a ±3±3 percentage point margin of error (this is very commonly used)? Use the previous sample as a pilot study to get p*. 

(You may need four decimal places in your critical value to solve this problem.)

Sample size:

 

 

4.

2.5758 

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 99% confidence interval for the proportion who are not satisfied.

(a) Past studies suggest that this proportion will be about 0.3. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015. 

(You will need a critical value accurate to at least 4 decimal places.) 

Sample size: 

 

(b) Using the sample size above, when the sample is actually contacted, 32% of the sample say they are not satisfied. What is the margin of the error of the confidence interval? 

MoE:

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