Create real life problem situations in psychological field that illustrates the use of each of the following probability and non- probability sampling techniques. 2. Cluster Sampling
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- An article appeared in the Journal of Gambling Issues, in which the authors looked at random samples of Ontario residents who (i) have not completed some form of post-secondary education and (ii) have completed some form of post-secondary education. The data: Did not Complete PS Education with gambling problem: 14 out of 255 sample Did complete PS Education with gambling problem: 9 out of 310 sample Let pNoPS represent the proportion of persons not completing some form of post-secondary education who have a gambling problem, and pPS be the proportion of persons having completed post-secondary education who have a gambling problem. (a) Find a 99% confidence interval for pNoPS−pPS, the difference in the proportion of gamblers among those who have not completed post-secondary education and those that have. Lower Bound of 99% CI = Upper Bound of 99% CI = (b) The confidence interval found in part (b) indicates that the proportion problem gamblers amongst those who have not completed post…Consider an experiment with sample space S = {A,B,C}.If P(A)=0.6, P(B)=0.2, and P(C)=0.2, then(a) P( B or C ) = (b) P( A and C ) =3. The dataset butterfat in the package faraway contains the average butterfat content (percent- ages) of milk for random samples of twenty cows, ten two-year old and ten mature (greater than four years old), from each of five breeds. Therefore, for each combination of breed and age categories, there are ten observations. The data are from Canadian records of pure-bred dairy cattle. Questions of interest are (i) if butterfat content differs with age and/or breed, and (ii) if any potential breed effect is the same for the two age groups. (a) Make appropriate plots of the data and comment on them. (b) Determine an appropriate model, and write it down mathematically, to answer the questions of interest. What are your conclusions? (c) Is the best breed in terms of butterfat content clearly superior to the second best breed? Justify.
- The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 58 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29μ=28.29 and ?=33.493σ=33.493, respectively. Let ?X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯x¯. Use the central limit theorem (CLT) to determine the probability ?P that the mean taxable wages in James' sample of 58 counties…You want to make a bar graph with 8 classes. Your lowest observed data point is 21 while your highest is 110. You want you lowest lower limit to be 20. What will be your lowest upper limit? You know that a sample space consists of events A, B, C and D. You also know that P(A) = P(B) = .24 and that P(C)= P(D). Find P(C).Part 1 of 4 A pharmaceutical company claims their new diabetes medication results in less variance in a patient's glucose level than if the patient were on no medication at all. An endocrinologist wishes to test this claim. He divides participants randomly into two groups. Group A consists of 20 diabetics who received the medication; group B consists of 25 diabetics who received a placebo. After two weeks, the blood sugar level of each patient in each group was measured with the following results (in mg/dL): Group A: 149.5, 178.9, 145.8, 195.4, 97.4, 123.4, 128.8, 121.1, 189.7, 134, 125, 93.7, 222.9, 115.5, 188.9, 87.6, 132.6, 109, 201.3, 93.1 Group B: 152.5, 138.5, 188, 52.9, 186.6, 154.3, 193, 150.1, 187.1, 122.1, 167.1, 112.2, 197.5, 131.8, 115.6, 166.2, 108, 141.3, 110.2, 164.5, 189.4, 142.2, 174, 190, 171.3 Perform a hypothesis test using a 5% level of significance to test the pharmaceutical company's claim. Step 1: State the null and alternative hypotheses. Но: 1 H.:Twins In 2000 The Journal of the American MedicalAssociation published a study that examined a sample ofpregnancies that resulted in the birth of twins. Birthswere classified as preterm with intervention (inducedlabor or cesarean), preterm without such procedures, or term or postterm. Researchers also classified the pregnan-cies by the level of prenatal medical care the mother received (inadequate, adequate, or intensive). The data,from the years 1995–1997, are summarized in the tablebelow. Figures are in thousands of births. (JAMA 284[2000]: 335–341)Is there evidence of an association between the durationof the pregnancy and the level of care received by themother? Twin Births, 1995–1997 (in Thousands)Preterm(induced orCesarean)Preterm(withoutprocedures)Term orpostterm Total Level ofPrenatal CareIntensive 18 15 28 61Adequate 46 43 65 154Inadequate 12 13 38 63Total 76 71 131 278Exhibit 11-5 The table below gives beverage preferences for random samples of teens and adults. Beverage Coffee Tea Soft Drink Other Teens 50 100 200 50 400 Adults 200 150 200 50 600 Total 250 250 400 100 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 11-5. The expected number of adults who prefer coffee isProblem #4: The manager at a clothing store would like to compare the sales of two employees, Employee A and Employee B. The daily sales (in S) for the two employees are recorded for random sample of days and some summary statistics are below: Problem #4(a): Problem #4(b): Problem #4(c): n X DOZA А 7 1515 419 11 1199 B S 202 We assume that the daily sales of each employee is normally distributed and they share a common variance. (a) What is the estimate of the common variance of their daily sales? (b) What is the critical value if we wish to conduct a test at 5% level of significance to determine if there is a difference in their true mean daily sales? (c) What is the p-value of the test? answer correct to 2 decimals answer correct to 3 decimals answer correct to 4 decimalsA local bus company is planning a new route to serve four housing subdivisions. Random samples of households are taken from each subdivision, and sample members are asked to rate, on a scale of 1 (strongly opposed) to 5 (strongly in favor), their reaction to the proposed service. The results are summarized in the accompanying table. Subdivision 1 Subdivision 2 Subdivision 3 Subdivision 4Ni 240 190 350 280ni 40 40 40 40x̄i 2.5 3.6 3.9 2.8si 0.8 0.9 1.2 0.7a. Find a 90% confidence interval for the mean reaction of households in subdivision 1.b. Using an unbiased estimation procedure, estimate the mean reaction of all households to be served by the new route. c. Find 90% and 95% confidence intervals…Rock-paper-scissors is a game played by two or more people where players choose either rock, paper, or scissors with their hands. For your statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data: Under the assumption that no option is favored, what would the expected number of paper be? a. 33 b. 20 c. Impossible to determine d. 21 e. 0.33 What is the test statistic for the chi-square goodness of fit test? a. 0.0005 b. 0 c. 0.30 d. 0.317 e. 0.20 f. 7.51QUESTION 8 A hotel employs 100 managers and staff. To ascertain their employees' opinions of a proposed health insurance plan, 30 employees are surveyed at random. The proportion of the sampled 30 employees who favor the health insurance plan represents a statistic in this scenario. O True O FalseSEE MORE QUESTIONS
