91Ó°ÊÓ

For a shipment of cable, suppose that the specifications call for a mean breaking strength of 2,000 pounds. A sampling of the breaking strength of a number of segments of the cable has a mean breaking strength of 1955 pounds with an associated standard error of the mean of 25 pounds. Using the 5 percent level, test the significance of the difference found.

A firm producing light bulbs wants to know if it can claim that its light bulbs last 1000 burning hours. To answer this question, the firm takes a random sample of 100 bulbs from those it has produced and finds that the average lifetime for this sample is 970 burning hours. The firm knows that the standard deviation of the lifetime of the bulbs it produces is 80 hours. Can the firm claim that the average lifetime of its bulbs is 1000 hours, at the \(5 \%\) level of significance?

Suppose it is required that the mean operating life of size "D" batteries be 22 hours. Suppose also that the operating life of the batteries is normally distributed. It is known that the standard deviation of the operating life of all such batteries produced is \(3.0\) hours. If a sample of 9 batteries has a mean operating life of 20 hours, can we conclude that the mean operating life of size "D" batteries is not 22 hours? Then suppose the standard deviation of the operating life of all such batteries is not known but that for the sample of 9 batteries the standard deviation is \(3.0 .\) What conclusion would we then reach?

A manufacturer of transistors claims that its transistors will last an average of 1000 hours. To maintain this average, 25 transistors are tested each month. If the computed value of \(\mathrm{t}\) lies between \(-t_{.025}\) and \(t_{025}\), the manufacturer is satisfied with his claim. What conclusions should be drawn from a sample that has a mean \(\overline{\mathrm{x}}=1,010\) and a standard deviation \(\mathrm{s}=60\) ? Assume the distribution of the lifetime of the transistors is normal.

A certain printing press is known to turn out an average of 45 copies a minute. In an attempt to increase its output, an alteration is made to the machine, and then in 3 short test runs it turns out 46,47, and 48 copies a minute. Is this increase statistically significant, or is it likely to be simply the result of chance variation? Use a significance level of \(.05\).

Two separate groups of subjects were tested. The experimental group (Group E) had 10 subjects; the control group (Group C) had 9 subjects. The data are given below; the scores are assumed to be normally distributed. Group E: \(12,13,16,14,15,12,15,14,13\), and 16 . Group C: \(10,13,14,12,15,16,12,14\), and 11 . Determine whether the means of the two groups differ significantly at the \(.05\) level of sionificance.

A sports magazine reports that the people who watch Monday night football games on television are evenly divided between men and women. Out of a random sample of 400 people who regularly watch the Monday night game, 220 are men. Using a \(.10\) level of significance, can be conclude that the report is false?

A manufacturer of car batteries guarantees that his batteries will last, on the average, 3 years with a standard deviation of 1 year. If 5 of these batteries have lifetimes of \(1.9,2.4,3.0\), \(3.5\), and \(4.2\) years, is the manufacturer still convinced that his batteries have a standard deviation of 1 year?

Suppose for the previous problem a sample of 15 operations is obtained and the sample mean of these operations is \(6.87\) minutes with a standard deviation of 4 minute. Would these results indicate that the worker deviates from the standard of \(6.4\) minutes at a \(1 \%\) level of significance?