Multiple Statistics Sample Size Questions

Question

1. A Pew survey, conducted by Princeton Survey Research International reports that 1063 of a sample of 2054 adults reported that they played video games. Construct a 95% confidence interval for the proportion of all adults who played video games? What is the sampling error (SE) for this interval?
2. A researcher is interested in estimating the average rent in a large city. She wants to be 90% confident. If the standard deviation is $200, how large a sample is needed to get the desired information and to be accurate within $100?
3. The quality control manager at a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process variance is known to be 10000 hours. A random sample of 64 light bulbs indicated a sample average of 350 hours. Construct a 90% confidence interval for the true average life of light bulbs in this shipment.
4. A meteorologist who sampled 15 cold weather fronts found that the average speed at which they traveled across a certain state was 18 miles per hour. The standard deviation of the sample was 2 miles per hour. Find a 95% confidence interval of the mean.

Answer 1

For #1) the confidence interval is (0.49592, 0.53914).

For #2) the answer is at least 11 people are needed to ensure the margin of error is within $100

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