MATH30LONG QUIZ 33rd QUARTER SY 2010-11SET CTest I. TRUE OR FALSE. Write STATISTICS if the statement is true and write PROBABILITY if the statement is false. (2 pts each)1. A small significance level indicates that the hypothesis will probably be not rejected.2. If the sample size is doubled, the level of significance naturally increases.3. The p-value is less than the significance level.4. The population mean is an example of a parameter.5. The p-value is a probability value.
6. The level of significance is equal to 1-level of confidence.7. Testing at 5% level of significance means that you only have a 5% chance of rejecting the null hypothesis.8. The sampling distribution of the sample mean is approximately normal if and only if the population is normal.9. If we would reject a null hypothesis at the 5% level, we would also reject it at the 1% level.10. The significance level is determined under the assumption that the alternative hypothesis is true.Test II. MULTIPLE CHOICE. Choose the best answer among the choices given. Write only the letter of your choice. (3 pts each)1. In testing H0: µ20 against H1: µ
20 when α=0.05, n=25, s2=16 and x=22, one should conclude that
a) µc) µ20 with 95% confidence d) µ
2. A sample of 40 students was considered to compare their grades in Algebra and Trigonometry. With a computed t-statistics of 2.63, what conclusion should you draw?a) There is a significant difference in the Algebra and Trigonometry grades, p0.005.
b) There is a significant difference in the Algebra and Trigonometry grades, pc) There is a significant difference in the Algebra and Trigonometry grades, pd) There is no significant difference in the two sets of grades.3. Given the null hypothesis "A new process is as good as or better than the old one". The Type I error is to conclude that:a) the old process is as good or better when it is notb) the old process is better when it isc) the old process is better when it is notd) the new process is as good or better when it is4. What is the probability of a Type II error when α=0.05?a) 0.025 b) 0.050 c) 0.950 d) 0.9755. In testing a hypothesis using a statistic Y, a critical region is chosen to meet which of the following conditions?I. The probability of Y falling in the critical region when the null hypothesis is true is α.II. The probability of Y falling in the critical region when the alternative hypothesis is true is greater than if not falling in the critical region.III. The sample size is large.a) I, II and III b) I and II only c) I only d) II onlyTEST III . PROBLEM SOLVING. Solve the following problems by showing complete and systematic solution. (15 pts each)1. The school canteen is conducting a study to find the amount spent on refreshments by the varsity players. They gather a simple random sample of 50 women and 100 men. For women, the average expenditure was P20 with a standard deviation of P3. For men, it was P15 with a standard deviation of P2. What is the 99% confidence interval for the spending difference between women and men players? Assume that the two populations are independent and normally distributed.2. The heights of 1000 students are approximately normally distributed with a mean of 174.5 cm and a standard deviation of 6.9 cm. If 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter, determine a) the mean and standard deviation of the sampling distribution of the sample mean; b) the number of sample means that fall between 172.5 and 175.8 cm.3. Prof X has been handling differential equations for several years already. As a way of checking his teaching methodologies and on the general effectiveness of the students in his classes from year to year, he has been administering the same assessment quiz during the fifth week of class. Over the years, the score has averaged 13.5. This term, he believes that his students are doing significantly different than usual. If he can establish support of his perception, he will alter his teaching methods for this class. On the basis of the test scores below, should he conclude that there is a support for his perception and change his methods? Assume normality and use α=0.05Scores: 20, 19, 6, 4, 3, 10, 13, 14, 16, 17, 10, 11, 8, 9, 11, 20, 18, 6, 4, 134. The Bowl Company has designed a new type of 16-lbs bowling ball. The company knows that the average man who bowls in a bowling league with the company's old ball has a bowling average of 155. The variance of these averages is 100. The company asks a random sample of 100 men bowling in scratch leagues to bowl for 5 weeks with their new ball. The mean of bowling averaged for these men with the new ball is 170. There is no reason to believe that the variance is any different with the new ball. Test the hypothesis that the new ball does not improve a bowler's average at the 5% level of significance.5. EMA Company has developed a new cell phone battery claimed to operate continuously for at least 7 hours longer than the old battery. To test the claim, the company randomly selects a sample of 100 new batteries and 100 old batteries. The old batteries run continuously for 190 hours with a standard deviation of 20 hours; the new batteries, 200 hours with a standard deviation of 40 hours. Test the company's claim at α=0.05 level.
MATH30 - Long Quiz 3 - 3rd Term - 20102011
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