A particular brand of dishwasher soap is sold in three sizes: 30 oz, 40 oz, and 60 oz. Twenty percent of all purchasers select a 30-oz box, 50% select a 40-oz box, and the remaining 30% choose a 60-oz box. Let X₁ and X₂ denote the package sizes selected by two independently selected purchasers. (a) Determine the sampling distribution of X. X 30 35 40 45 50 60 P(x) Calculate E(X). E(X) = Compare E(X) to μ. O E(X) = μ O E(X) > H Ο Ε(Χ) < με (b) Determine the sampling distribution of the sample variance S². 0 50 200 s² p(s²) Calculate E(S²). E(S²) = Compare E(S2) to σ². O E(S²) > 0² O E(S²) = 0² O E(S²) < 0² oz 450
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- A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging machine will lower the proportion of bags that are damaged. The company selected a random sample of 150 bags from the old machine and found that 15 percent of the bags were damaged, then selected a random sample of 200 bags from the new machine and found that 8 percent were damaged. Let pˆOp^O represent the sample proportion of bags packaged on the old machine that are damaged, pˆNp^N represent the sample proportion of bags packaged on the new machine that are damaged, pˆCp^C represent the combined proportion of damaged bags from both machines, and nOnO and nNnN represent the respective sample sizes for the old machine and new machine. Have the conditions for statistical inference for testing a difference in population proportions been met? No, the condition for independence has not been met, because random samples were not selected. A No, the…Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. A random sample of 1900 women from the first country yielded 513 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 515 women with iron-deficiency anemia. Can we conclude, at the 0.10 level of significance, that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the values of the test statistic. c. FInd the p-value. d. Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?Two investigators have studied the income of a group of persons by the method of sam-pling. The following table gives their findings Investigator Poor Middle Class Well-to-do TotalA 160 30 10 200B 140 120 40 300Total 300 150 50 500 Using Chi-squared test, show that the sampling technique of at least one of the investi-gators is a suspect at 5% level of significance.
- A particular brand of dishwasher soap is sold in three sizes: 25 oz, 35 oz, and 60 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 35-oz box, and the remaining 30% choose a 60-oz box. Let X1 and X2 denote the package sizes selected by two independently selected purchasers. (a) Determine the sampling distribution of X. x 25 30 35 42.5 47.5 60 p(x) Calculate E(X). E(X) = ozCompare E(X) to ?. E(X) > ? E(X) < ? E(X) = ? (b) Determine the sampling distribution of the sample variance S2. s2 0 50 312.5 612.5 p(s2) Calculate E(S2).E(S2) = Compare E(S2) to ?2. E(S2) = ?2 E(S2) > ?2 E(S2) < ?2A domestic manufacturer of watches purchases quartz crystals from a Swiss firm. Thecrystals are shipped in lots of 1000. The acceptance sampling procedure uses 20 randomlyselected crystals.a. Construct operating characteristic curves for acceptance numbers of 0, 1, and 2.b. If p0 is .01 and p1 = .08, what are the producer’s and consumer’s risks for each sampling plan in part (a)?In analyzing the consumption of cottage cheese by members of various occupational groups, the United Dairy Industry Association found that 326 of 837 professionals seldom or never ate cottage cheese, versus 220 of 489 white-collar workers and 522 of 1243 blue-collar workers (Sheet 53). Assuming independent samples, use the 0.03 level in testing the null hypothesis that the population proportions could be the same for the three occupational groups. Sheet 53 Group 1 Group 2 Group 3 Total seldom or never 326 220 522 1068 often 511 269 721 1501 Total 837 489 1243 2569 Select one: a) chi-square stat = 4.81, crit. value = 7.01, fail to reject H0, population proportions are not different b) p-value = 0.09, reject H0, population proportions are not different c) chi-square stat = 4.81, crit. value = 9.2, fail to reject H0, population proportions are not different d) p-value = 0.029, reject H0, population proportions different
- 1) A cement producer, manufactures and then fills 40kg-bags of powder cement on twodistinct production tracks located in separate suburbs. To determine whether differencesexist between the average fill rates for the two tracks, a random sample of 25 bags fromTrack 1 and a random sample of 16 bags from Track 2 were recently selected. Each bag’sweight was measured and the following information measures from the samples arereported:Production ProductionTrack 1 Track 2n1 = 25 n2 = 16x2 = 40.02 x1 = 39.87 s1 = 0.59 s2 = 0.88 Supervision believes that the fill rates of the two tracks are normally distributed with equalvariances.Construct a 95% confidence interval estimate of the true mean difference between the twotracks.--------------------------------------------------------------------------------------------------------------2) Two independent simple random samples were selected from two normallydistributed populations with unequal variances yielded the following information:Sample 1…An experiment in teaching research methods in psychology was recently conducted at a large university. One section was taught by the traditional lecture-lab method, a second was taught by an all-lab/demonstration approach with no lectures, and a third was taught entirely by a series of videotaped lectures and demonstrations that the students were free to view at any time and as often as they wished. Students were randomly assigned to each of the three sections, and, at the end of the semester, random samples of final exam scores were collected from each section. Test whether teaching method affected student performance on the final exam. Use the .05 significance level. What is the null hypothesis? Lecture/Lab All-Lab/Demo Videotaped M1=70.67 M2=72.33 M3=65.33 S1=2.95 S2=3.29 S3=1.20 N1=5 N2=5 N3=5 Group of answer choices The mean final exam score for Videotaped is lower than the mean final exam scores for Lecture/Lab and All-Lab/Demo The mean final exam score for…An experiment in teaching research methods in psychology was recently conducted at a large university. One section was taught by the traditional lecture-lab method, a second was taught by an all-lab/demonstration approach with no lectures, and a third was taught entirely by a series of videotaped lectures and demonstrations that the students were free to view at any time and as often as they wished. Students were randomly assigned to each of the three sections, and, at the end of the semester, random samples of final exam scores were collected from each section. Test whether teaching method affected student performance on the final exam. Use the .05 significance level. What is the correct decision and conclusion? Lecture/Lab All-Lab/Demo Videotaped M1=70.67 M2=72.33 M3=65.33 S1=2.95 S2=3.29 S3=1.20 N1=5 N2=5 N3=5 Group of answer choices Decision: Do not reject the null hypothesis; Conclusion: The mean final exam scores for the three teaching methods are different…
- An experiment in teaching research methods in psychology was recently conducted at a large university. One section was taught by the traditional lecture-lab method, a second was taught by an all-lab/demonstration approach with no lectures, and a third was taught entirely by a series of videotaped lectures and demonstrations that the students were free to view at any time and as often as they wished. Students were randomly assigned to each of the three sections, and, at the end of the semester, random samples of final exam scores were collected from each section. Test whether teaching method affected student performance on the final exam. Use the .05 significance level. What cutoff score(s) should be used? Lecture/Lab All-Lab/Demo Videotaped M1=70.67 M2=72.33 M3=65.33 S1=2.95 S2=3.29 S3=1.20 N1=5 N2=5 N3=5 Group of answer choices +3.68 +3.89 +3.74 +3.81 PreviousNextIn a breeding experiment, chicken with white feathers, small comb were mated and the offspring categories white feathers, small comb (WS), white feathers. large comb (WL), dark feathers, small comb (DS) and dark feathers, large comb (DL) were expected to follow the ratio 9:3:3:1 the researcher observed that there were 100 WS, 32 WL, 40 DS and 20 DL offspring. In order to test if the observed frequencies follow the expected ratio, what should be the hull hypothesis?A. P(WS) = 100/192, P(WL) = 32/192, P(DS) = 40/192 , P(DL) = 20/192 B. P(WS) = 100 , P(WL) = 32, P(DS) = 40, P(DL) = 20 C. P(WS) = 9/16 , P(WL) = 3/16, P(DS) = 3/16, P(DL) = 1/16 D. P(WS) = 9, P(WL) = 3, P(DS) = 3 , P(DL) = 1 2. In Problem 1, what would be the degree of freedom for an appropriate test?A.2 B.3 C.4 D.1 3. What is the value of the computed test statistic in problem 1? A.7.81 B.3.84 C.6.81 D.5.99 5.What would be the p-value for this test in problem 1? A.0.28 B.0.05 C.0.08 D. 0.11 6. At 5-% level of significance,…In a population where 67%67% of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer candidate A to be normally distributed? In a population where 46%46% of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer candidate A to be normally distributed?