1. To find the 98% confidence interval for the population mean, for a situation in which n is greater than 30, what Z value would you use? Hint: do not use the Z table or your calculator to find this value. Express your answer to three places of decimal and state the positive value only. Note that you are unlikely in the 'non-school' world to actually want the 98% confidence interval and that you can answer this question most easily by using the t table.
2. x-bar = 18.40, s = 5.62, n = 35. The shape of the underlying population is not normally distributed. Find the 95% confidence interval for µ and enter the LOWER boundary of this interval as your answer rounded to two places of decimal.
3. In question 2, what size sample would be necessary to estimate the true value of the population mean to within 1.25 units with 95% confidence? (Note that "within 1.25 units" means the interval you find will have a width of 2.50 units.)
4. You want to be able to state that the population mean is lower than some value with 95% confidence. What t value would be used to find the 95% one-tailed confidence interval for the population mean when n = 12 and the population is known to be normally distributed? Express your answer with 3 places of decimal. Note that confidence intervals are always two-tailed unless, as in this case, otherwise specified.
5. Given that x-bar = 18.60, s = 3.48, n = 18, and the population is known to be normally distributed, find the LOWER boundary of the 95% confidence interval for µ. Express your answer with 2 places of decimal. Note that confidence intervals are always two-tailed unless otherwise specified.
6. To find the 90% confidence interval for the population variance when n = 15 and the population is known to be normally distributed, what values of chi-squared would you use?
7. Find the 98% confidence interval for the population variance when n = 23, s = 23.48 and the population is known to be normally distributed. Enter only the LOWER boundary of your interval as your answer, rounded to 2 places of decimal.
8. Find the 98% confidence interval for the population variance when n = 23, s = 23.48 and the population is known to be normally distributed. Enter only the LOWER boundary of your interval as your answer, rounded to 2 places of decimal.
9. In the situation considered in question 8, what size sample would be necessary to find, with 95% confidence, the true proportion to within 5%? You may wish to use your memory function to store the p-hat value.
10. What size sample would be necessary to find, with 95% confidence, the true population proportion to within 3.5% if you had no idea what the true proportion was? This question stands alone and does not refer to any other question.