Self Test 7 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.
Tests of Means and Proportions Using Normal Distributions
1.True False. The mean life time of a sample of light bulbs produced by a certain company is computed to be 1550 hours with a standard deviation of 120 hours. If m is the mean lifetime of all the bulbs produced by the company, test the hypothesis m=1600 hours against the alternative hypothesis m¹1600 hours, using 5% level of significance.
a)Reject
2. True False. In problem 1 test the hypothesis m=1600 hours against the alternative m<1600, using a 5% level of significance.
a) Reject
3.True False. A test was given to two classes consisting of 50 and 60 students respectively. In the first class the mean grade was 75 with standard deviation of 8. In the second class the mean grade was 78 with standard deviation of 7. Is the performance of the two classes significantly different at 1% and 5% level?
(a)No difference at both 1% and 5% significance level
4.True False. In the past a machine produced pieces of equipment with a mean thickness of 0.060 inches. To determine whether the machine is in the proper working condition, a sample of ten pieces of equipment is chosen for which the mean thickness is 0.063 and the standard deviation is 0.003 inches. Test the hypothesis that the machine is in the proper working condition using a level of significance 0.05 and 0.01.
Reject at 5% and fail to reject at 1% significance level.
5.True False. In the past the standard deviation of weights of certain 40.0 gram packages filled by a machine was 0.25 grams. A random sample of 30 packages showed a standard deviation of 0.32 grams. The apparent increase is in variability significant at 0.05 level?
6.True False. A professor has two classes, X and Y. Class X had 16 students and class Y has 25 students. On the same test, although there was no significant difference in mean grades, class X had a standard deviation of 10 while class Y had a standard deviation of 13. We ca conclude at 1% level of significance, that the variability of class Y is greater than that of X?
7.True False. In 200 tosses of a coin, 116 heads and 84 tails were observed. Can we fail to reject testing the hypothesis that the coin is fair using a level of significance of 0.05.