For Problems 3–11, please provide the following information.
- (a) What is the level of significance? State the null and alternate hypotheses.
- (b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution?
- (c) Find or estimate the P-value of the sample test statistic.
- (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
- (e) Interpret your conclusion in the context of the application.
- (f) Find the requested confidence interval for the population variance or population standard deviation. Interpret the results in the context of the application.
In each of the following problems, assume a
Law: Bar Exam A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between “better,” “average,” and “poorer” students. A group of attorneys in a Midwest state has been given the task of making up this year’s bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 24 newly graduated law students. Their scores give a sample standard deviation of 72 points.
- (i) Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.
- (ii) Find a 99% confidence interval for the population variance.
- (iii) Find a 99% confidence interval for the population standard deviation.
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Bundle: Understandable Statistics, Loose-leaf Version, 12th + WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term
- What is meant by the sample space of an experiment?arrow_forward4. Ms Julia Palac is an instructor in Statistics. She gave an examination before and after he discussed the topic "hypothesis testing" and gathered the following data: Studen Score before Score after Discussion Discussion 1 81 85 2 87 90 3 70 75 4 89 93 5 85 88 At a = 0. 01 level of significance, is the learning effective?arrow_forwardOur professor wants us to calculate the test statistic and p-value by hand. The test statistic is correct. I can't get the p-value to save my life. Do you know what I am doing wrong?? (All of these p-value answers are incorrect: 0.25, .1230, 2.32, .0232, .02, and .01) An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of ?=78 college students found 30 who had brown eyes.Consider testing ?0:?=.45??:?≠.45 (a) The test statistic is ? = -1.16 (b) P-value =arrow_forward
- A cigarette manufacturer claims that his cigarettes have nicotine content that does not exceed 2.0 milligrams. If a random sample of 10 cigarettes of this type have nicotine contents of 2.0, 2.3 1.7, 2.2, 1.9, 2.2, 2.0, 2.5, 2.1 and 1.9 milligrams, would you agree with the manufacturer's claim? a = 0.05, what is the computed test statistic for this problem? A none of the choices B) 1.10 C) 2.306 D) 1.1833arrow_forwardA cigarette manufacturer claims that his cigarettes have nicotine content that does not exceed 2.0 milligrams. If a random sample of 10 cigarettes of this type have nicotine contents of 2.0, 2.3 1.7, 2.2, 1.9, 2.2, 2.0, 2.5, 2.1 and 1.9 milligrams, would you agree with the manufacturer's claim? a = 0.05 what is the correct set of hypotheses to test this claim? (A) H0μΣ 2.0 ; H1: μ 2.0 C) HO:μ= 2.0; H1: μ .0 D HO:µ < 2.0; H1: µ 2 2.0arrow_forwardA cigarette manufacturer claims that his cigarettes have nicotine content that does not exceed 2.0 milligrams. If a random sample of 10 cigarettes of this type have nicotine contents of 2.0, 2.3 1.7, 2.2, 1.9, 2.2, 2.0, 2.5, 2.1 and 1.9 milligrams, would you agree with the manufacturer's claim? a = 0.05 what is the correct set of hypotheses to test this claim? A HO:µ 2.0 D) H0:μ= 2.0; H1: μ + 2.0arrow_forward
- Dr. Kijowski is concerned about student phone use, so she collects information on the number of text messages that each student sent on a particular day. The boxplot below shows the results. Based on the boxplot, which of the following is the most reasonable conclusion? a. There are more people with data values below the median than there are people with data values above the median. Selected:b. There are more people with data values between the first quartile and the median than there are people with data values between the median and the third quartile.This answer is incorrect. c. There are fewer people with data values between the first quartile and the median than there are people with data values between the median and the third quartile. d. There are approximately the same number of people with data values between the first quartile and the minimum as there are people with data values between the third quartile and the maximum. e. The data are less spread out between the…arrow_forwardThe test for the equality of two population variances is based on which of the following? a The ratio of the two sample variances. b The difference between the two population variances. c The difference between the two sample variances. d The ratio of the population variances to the sample variances.arrow_forwardSarah thinks that she has lost interest in online shopping. Based on her shopping history, she can see that her average purchases in the past were about 4 items on average each week. Since this last month, she can now see that she has only purchased 2 items on average each week, (with a SD of 1). To determine whether her shopping habits have changed, what statistical test should be used here?arrow_forward
- This Question from Course Applied Statistical Methodsarrow_forwardWhat is the degree of freedom (sd) in the analysis of a 4-by-5-dimensional table that is summarized by counting the data? Please select one: a. 12 b. 18 c. 19 d. 15 e. 20arrow_forwardPlease help me in the following question.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning