2-25. Let A and B be the two possible outcomes of an experiment and suppose P(B)=p and P(A) = 0-4, (i) For what choice of p are A and B mutually exclusive? (ii) For what choice of p are A and B independent ? P (AU B) = 0-7
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- Let A and B be the two possible outcomes of an experiment and suppose P(A) = 0.4, P(AUB) = 0.7 And P(B) = P. (i) For what choice of p are A and B mutually exclusive? (ii) For what choice of p are A and B independent?Q2.6. (based on Problem 2.33; page 52) (1) If a multiple-choice test consists of 7 questions, each with 4 possible answers of which only 1 is correct,: a. in how many different ways can a student check off one answer to each question? b. in how many ways can a student check off one answer to each question and get all the answers wrong?. Suppose an exam consists of multiple-choice questions, with each question having 5 options. Exactlyone of the five options is the correct answer. Suppose 24 points are awarded for a correctly answeredquestion.(a) How many points should be deducted for an incorrectly answered question, so that for a studentguessing randomly, the expected score on a question is zero?(b) If a student is able to correctly eliminate one option as a possible correct answer but is still guessingrandomly, what happens to his/her expected score for that question? Use your answer to (a) asthe number of points being deducted for an incorrect answer.
- Bonnie and her friends are dubious that a new abdominal exercise machine is as effective as its commercial claims. They decide to conduct an experiment to find out. For three months, Bonnie has 25 randomly chosen friends use the new machine, and 25 others do traditional abdominal exercises. At the end of the experiment, she counts the number of sit-ups each friend can do in one minute. No. of sit-ups for friends who use machine 43 29 41 22 43 28 35 26 31 48 41 24 48 25 23 35 25 28 28 31 27 45 41 22 46 Mean: 33.4 sit-ups No. of sit-ups for friends who do traditional exercises 44 33 33 24 49 39 21 45 44 48 47 50 43 46 29 46 45 32 36 41 49 45 28 49 29 Mean: 39.8 sit-ups How much lower is the average for the treatment group than the average for the control group? sit-upsTwo new accessions of pepper were tested for pungency. The two accessions were given to ten persons who scored the pepper samples as 1 if it is the more pungent of the two and 0 , otherwise. Which test can be conducted to compare pungency of the two new accessions? a. F-test B. Friedman C. t-test D. sign testPlease provide a neat solution thank you!
- The market shares in 2012 of four (4) television companies, A, B, C and D are listed below. A survey was carried out in 2017 on 200 television buyers and the distribution of buyers to A, B, C and D are also listed in the last column. Company Market Share in 2012 Number of buyer in 2017 A 0.4 70 B 0.32 60 C 0.24 54 D 0.04 16 (a) Specify the competing hypotheses to test whether the market shares have changed since 2012. (b) Calculate the value of the test statistics. (c) Use ? = 0.05 to determine if the market shares have changed since 2012.Question 10: give the conclusion.A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n =10 adolescents (aged 12-17) and a sample of n =6 adults (aged 25-32). The researcher finds that the average time spent around friends for adolescents is M1= 3 hours with a SS1 of 44. He also finds that the average time spent around friends for adults is M2= 2 hours with a SS2 of 40. a. Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? b. What is the variance? c. What is the estimated standard error? d. What is the value of the t statistic? e. Do we reject or fail to reject the null hypothesis (α = .01)? Why? f. Calculate and report the variance explained ( r2)
- Step 1: Write down your null and alternative hypotheses. Use p1 to represent the proportion of the population who preferred Brand 1 over the other two brands, and p2 to represent the population proportion for Brand 2 and p3 for Brand 3. H0: Ha: Group of answer choices Null: There is a preference for one or more brands, that is p’s are not all equal. Alternative: There is no brand preference, that is p1 = p2 = p3 = 1/3; Null: There is no brand preference, that is p’s are not all equal. Alternative: There is a preference for one or more brands, that is p1 = p2 = p3 = 1/3; Null: There is no brand preference, that is p1 = p2 = p3 = 1/3; Alternative: there is a preference for one or more brands, that is p’s are not all equal. Null: There is a preference for one or more brands, that is p1 = p2 = p3 = 1/3; Alternative: There is no brand preference, that is p’s are not all equal.A researcher is interested in understanding if there is a difference in the proportion of undergrad and grad students at UCI who prefer online teaching to in person teaching, at the a = 0.05 level. They take 2 samples, first, a sample of 300 undergrad students. The second, is a sample of 172 grad students. Of the undergrads, 186 said they preferred online lectures, and of the graduate students, 104 said that they prefer online lectures. Let p₁ = the proportion of undergrad students who prefer online class and p2 = the proportion of grad students who prefer online lectures. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem). (b) Calculate the test statistic. (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic under Ho. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at…7. A new drug study was conducted by a drug company. In the study, 10 people were chosen at random to take Vitamin X for 3 months and then have their cholesterol levels checked. In addition, 10 different people were randomly chosen to take Vitamin Y for 3 months and then have their cholesterol levels checked. All 20 people had cholesterol levels between 8 and 10 before taking one of the vitamins. The drug company wanted to see which of the 2 vitamins had the greatest impact on lowering people's cholesterol. The following data was collected: Vitamin X 7.27.5 5.2 6.5 7.7 10 6.47.6 7.77.8 Vitamin Y 4.8 4.44.5 5.1 6.5 8.03.1 4.6 5.2 6.1 (a) Draw a box-and-whisker plot for both sets of data on the same number line. (b) Use the double box-and-whisker plots to compare the 2 vitamins and provide a conclusion for the drug company. (e) State the skewness of both distributions and justify your answer.