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Sample Statistics Problems

1. A survey of 400 people who took vacations revealed that 242 of them flew to their destination. Give a 95% confidence interval for the percentage of all people who fly when they take a trip. Does it appear statistically correct to conclude that more than 50% of all people who take vacations will fly to their destination? Why or why not?

2. Suppose you want to estimate the percentage of adults who fly to their vacation destination and you want your estimate to be within 3 percentage points of the correct population measure, based upon a 95% confidence level. What size sample is required?--(assume that no estimate of "p-hat" is known.)

3. The average systolic blood pressure readings from a random sample of 100 people is 123.4 (assume a population standard deviation of 15.6). Based upon a desired 99% confidence level, determine the margin of error E in this sample statistic and then give the associated confidence interval.

4. You need to estimate the mean useful life of a certain brand of light bulb to within 20 hours with 98% confidence. Previous studies indicate that the standard deviation for the light bulb is 40 hours. How many observations should your sample contain to meet this desired level of accuracy?

Solution Preview

Hi there,

1. The critical value for 95% confidence interval is 1.96
p = 242/400 = 0.605
margin of error = 1.96*sqrt(0.605*(1 -0.605)/400) = 0.048
upper limit: 0.605 + 0.048 = 0.653
lower limit: 0.605 - 0.048 = 0.557
Therefore, the 95% confidence interval is [0.557, 0.653].
Since all values in the ...

Solution Summary

Sample statistics problems are examined for the average systolic blood pressure reading.