Self Test 6 for Probability
and Statistics
This test was constructed by Zauresh Atakhanova based on the Schaum's Outline Theory and Problems of Probability and Statistics by Murray R. Spiegel. If you need more review refer also to this outline.
1. True False Give an example of estimators (or estimates) which are (a) unbiased and efficient, (b) unbiased and inefficient, (c) biased and inefficient.
a) sample mean
b) sample median
c) sample standard deviation
Confidence Interval Estimates for Means (Large Samples)
2.True False. Measurements of the diameters of a random sample of 196 ball bearings made by a certain machine during one week showed a mean of 0.724 inches and a standard deviation of 0.042. Find (a) 95% and (b) 99% confidence interval for the mean diameter of all the ball bearings.
a) 0.724+/-0.0077
b) 0.724+/-0.0058
Confidence Interval Estimates for Means (Small Samples)
3.True False. The 95% confidence coefficients (1.96 “two-tailed”) for the normal distribution are given by +/-1.96. What are the corresponding coefficients for the t distribution if (a) v=9, (b) v=30?
(a) +/-2.26
(b) +/-2.04
4.True False. A sample poll of 1000 voters chosen at random from all voters in a given district indicated that 45% of them were in favor of a particular candidate. Find (a) 95%, (b) 99% and (c) 99.73% confidence limits for the proportion of all the voters in favor of this candidate.
(a) 0.45+/-0.0106
(b) 0.45+/-0.0157
(c) 0.45+/-0.0472
5.True False. A sample of 150 brand A light bulbs showed a mean lifetime of 1500 hours and a standard deviation of 1300 hours. A sample of 200 brand B light bulbs showed a mean lifetime of 1200 hours and a standard deviation of 80 hours. Find (a) 95% and (b) 99% confidence limits for the difference of the mean lifetimes of the populations of brands A and B.
a) 200+/-20.8
b) 200+/-28.6
6.True False. The standard deviation of the lifetimes of a sample of 200 electric light bulbs was computed to be 150 hours. Find (a) 95% and (b) 99% confidence intervals for the standard deviation of all such light bulbs.
a) 150+/-5.3
b) 150+/-8.7
7.True False.Work problem 5 using small sampling theory.
(a) (136.86, 167.03)
(b) (133.42, 173.88)
8.True False. Two samples of sizes 15 and 10 are drawn at random from two normal populations. If their variances are found to be 24 and 16 respectively, with 90% confidence interval for the ratio of the variances is (0.4804, 3.7451)