MATH 12 EXAM #3

NAME:____________________________________

For all problems provide the following as warranted. SHOW ALL WORK: Null hypothesis; Alternative hypothesis; appropriate variables such as variance, sample mean etc; a sketch of the normal distribution curve with the appropriate critical value(s), critical (reject) area(s), and test value shown; a written statement on whether the null hypothesis is to be reject based on the provided evidence. Please ask for clarification on these directions if needed. 1) Nationally 61.2% of federal prisoners are serving time for drug offenses. A warden

feels that in his prison the percentage is even higher. He surveys 260 randomly selected inmates’ records and finds that 100 of the inmates are not drug offenders. At

� = 0.02, is he correct?

2) A random sample of the number of games played by individual HS scoring leaders is

shown. Is there sufficient evidence to conclude that the variance in games played is

less than 25? Use � = 0.005. Assume the variable is normally distributed. 56 54 60 52 70 62 66 57 61 65

3) A random sample of 60 four member families in a walk-in movie theater revealed an average bill of $66.33 per family. The population standard deviation is $20.77. Estimate the mean bill for all four member families from the walk-in theater with 96% confidence.

4) The number of people who belong to a southern California golf club at each of several randomly selected small cities is shown here. Estimate the true population mean size of a small city golf club with 80% confidence. 71 68 32 51 88 30 39 30 57 47 33 35 46 55 41 44 32 47

5) A travel agent claims that the average number of rooms in hotels in a large city is

655. At � = 0.01, is the claim realistic? The data for a random sample of seven hotels are shown.

728 368 684 477 598 401 618

6) A researcher wishes to see if the average number of vacation days executives take per year is greater than 10. A random sample of 37 executives at a large company had a mean of 12. . The standard deviation of the population is 2.3. Is there enough

evidence to support the researcher’s claim at � = .01.