Q11. The director of quality at a light bulbs factory needs to estimate the average life of a large

shipment of light bulbs. A random sample of 64 light bulbs indicated a sample average life of 350

hours with a sample standard deviation of 100 hours.

a) Construct and interpret a 95% confidence interval estimate of the true average life of light

bulbs in this shipment.

b) Do you think the manufacturer has the right to state that the light bulbs last an average of

400 hours? Explain.

c) Does the population have to be normally distributed here for the interval to be valid?

Explain.

d) Explain why an observed value of 320 hours is not unusual, even though it is outside the

95% confidence interval you have calculated.

e) Suppose that the sample average had been 300 hours. What would be your answer to a) ?

Q12. A newspaper headline describing a poll of registered voters taken two weeks before a recent

election reads "Aitchison leads with 52%." The accompanying article describing the poll stated that

the margin of error was 2% with 95% confidence.

(a) Explain in plain language to someone who knows no statistics what "95% confidence"

means.

(b) The poll shows Aitchison leading. But the newspaper article said that the election was too

close to call. Explain why.

Q13. Twelve volunteers were assigned at random to each of three weight-loss plans. It can be

assumed that the 36 volunteers resemble a random sample from the population of all people who

would try a weight-loss program. Below are the number of pounds lost by each person in the

program. Test the null hypothesis that there is no difference in the expected weight loss for the three

programs. Give the appropriate hypotheses, your decision rule, test statistic value, and conclusion.

Use alpha = 0.05.

Plan A: 2,17,12,4,5,25,4,6,26,21,8,6

Plan B: 17,15,3,19,5,14,5,6,19,4,9,7

Plan C: 29,5,25,3,25,32,28,24,11,36,7,20

Q14. A random sample of recent stream flow rates at a watershed is to be compared with a sample

of flow rates taken earlier. Has the variability of the flow rates changed from earlier times to recent

times? You may use either of the two tests we discussed to test this. Give the appropriate hypotheses,

your decision rule, test statistic value, and conclusion. Use alpha = 0.05.

Earlier Flow Rates: 39,21,58,46,30,22,17,19

Recent Flow Rates: 32,36,41,27,35,48,31,28

Q15. The experiment randomized rats to three diets: control, low isoflavones, and high isoflavones. Here are the data: Treatment BMD (g/cm=) Control 0.228 0.207 0.234 0.220 0.217 0.228 0.209 0.221 0.204 0.220 0.203 0.219 0.218 0.245 0.210 Low dose 0.211 0.220 0.211 0.233 0.219 0.233 0.226 0.228 0.216 0.225 0.200 0.208 0.198 0.208 0.203 High dose 0.250 0.237 0.217 0.206 0.247 0.228 0.245 0.232 0.267 0.261 0.221 0.219 0.232 0.209 0.255 (a) Use the Kruskal-Wallis test to compare the three diets. (b) How do these results compare with what you find using the ANOVA F statistic