8. You want to design a study to estimate the proportion of students on your campus who agree with the statement "The student government is an effective organization for expressing the needs of students to the administration." You will use a 95% confidence interval and you would like the margin of error to be 0.05 or less. In previous years, it has been noted that the 32% of the campus agree with the statement. The minimum sample size required is approximately *

22

1795

271

335

9. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times, and the mean x of the n weighing is computed. Suppose the scale readings are normally distributed with unknown mean and standard deviation = 0.01 grams. How large should n be so that a 95% confidence interval for has a margin of error of 0.0001? *

385.

10,000.

100.

38, 416.

10. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2006. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006. *

375 2.33 81/30

375 2.575 9/30

375 2.575 81/30

375 2.756 81/30

11. An industrial designer wants to determine the average amount of time it takes an adult to assemble an "easy to assemble" toy. A sample of 16 times yielded an average time of 19.92 minutes, with a sample standard deviation of 5.73 minutes. Assuming normality of assembly times, provide a 95% confidence interval for the mean assembly time. *

19.92 3.02

19.92 2.51

19.92 3.05

19.92 2.81.

12. Other things being equal, the margin of error of a confidence interval increases as *

the sample mean increases.

the confidence level decreases.

the population standard deviation increases.

the sample size increases.

13. "What are the possible values of x-bar for all samples of a given n from this population?" To answer this question, we would need to look at the: *

z-scores of several statistics

sampling distribution

test statistic

standard normal distribution

14. In exploring possible sites for a convenience store in a large neighborhood, the retail chain wants to know the proportion of ratepayers in favour of the proposal. If the estimate is required to be within 0.1 of the true proportion, would a random sample of size n = 100 from the council records be sufficient for a 95% confidence interval of this precision? *

Yes.

No, because the length of the confidence interval would be greater than 0.1.

There is not enough information to answer this question.

No, because n, the sample size, is too small.

15. What is the smallest sample size required to provide a 95% confidence interval for a mean, if it important that the interval be no longer than 1cm? You may assume that the population is normal with variance 9cm2. *

n = 139.

n = 1245

n = 95

n = 34.