Consider the sample space S={ copper, sodium, nitrogen, potassium, uranium, oxygen, zinc), and the events A=[copper, sodium, oxygen) B=[sodium, nitrogen, potassium, zinc) C= {oxygen, nitrogen} Match column 1 to column 2 Prompts Submitted Answers A' {nitrogen, potassium, uranium, zinc) AUC (copper, sodium, oxygen, nitrogen) B' and C Choose a match ANBNC (AnB') UC' Choose a match
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- Let X1 and X2 constitute a random sample from a nor-mal population with σ2 = 1. If the null hypothesis μ = μ0 is to be rejected in favor of the alternative hypothesis μ = μ1 > μ0 when x > μ0 + 1, what is the size of the criti-cal region?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?Let X1, …, Xn be a random sample from a population with the Poisson(λ) distribution. Find the MLE of λ.
- 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…Suppose a simple random sample of size n equals 1000 is obtained from a population whose size is N equals 2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.75. Complete parts (a) through (c) below.If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that ni=1X2inis an unbiased estimator of σ2.
- Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet. In population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. Let pDrepresent the sample proportion for D, and let pE represent the sample proportion for E. (a) What is the value of the difference pD - pE? Show your work. (b) What are the mean and standard deviation of the sampling distribution of the difference in sample proportions pD - pE? Show your work and label each value. (c) Can it be assumed that the sampling distribution of the difference of the sample proportions pD - pE is approximately normal? Justify your answer.Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variablesSuppose a simple random sample of size n = 125 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified characteristic is p = 0.6
- Suppose a simple random sample of size n=125 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p= 0.4Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]Suppose x has a distribution with μ = 10 and σ = 2.A button hyperlink to the SALT program that reads: Use SALT.(a) If a random sample of size n = 44 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.)μx = σ x = P(10 ≤ x ≤ 12) = (b) If a random sample of size n = 66 is drawn, find μx, σ x and P(10 ≤ x ≤ 12). (Round σ x to two decimal places and the probability to four decimal places.)μx = σ x = P(10 ≤ x ≤ 12) =