Question
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
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
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