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Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: ni = 35, X1 = 53.9, n2 = 48, K2 = 71.8, S1 = 6 S2 = 10.8 Find a 95.5% confidence interval for the difference ui – u2 of the means, assuming equal population variances. Confidence Interval = ||

Suppose that Y1.... ,Y, is an i.i.d. random sample from a population with mean My and variance of. Let be the sample mean and sy the sample standard deviation. Which is the correct formula for the standard error of ?

Assume that you have a sample of n1=9​, with the sample mean X1=45​, and a sample standard deviation of S1=6​, and you have an independent sample of n2=16 from another population with a sample mean of X2=37​, and the sample standard deviation S2=5. Construct a 99​% confidence interval estimate of the population mean difference between μ1 and μ2. Assume that the two population variances are equal. ( ) ≤ μ1 −μ2 ≤ ( ) ​(Round to two decimal places as​ needed.)

Assume that you have a sample of n1=9​, with the sample mean X1=42​, and a sample standard deviation of S1=6, and you have an independent sample of n2=16 from another population with a sample mean of X2=35 and the sample standard deviation S2=7. Complete parts​ (a) through​ (d) below. a. What is the value of the​ pooled-variance tSTAT test statistic for testing H0: μ1=μ2​ tSTAT equals = ​(Round to two decimal places as​ needed.)

Sample annual salaries​ (in thousands of​ dollars) for employees at a company are listed. 43, 54, 55, 51, 33, 33, 43, 54, 55, 26, 51, 43, 46 ​(a) Find the sample mean and sample standard deviation. ​(b) Each employee in the sample is given a​ $3000 raise. Find the sample mean and sample standard deviation for the revised data set. ​(c) Each employee in the sample takes a pay cut of ​$2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set. ​(d) What can you conclude from the results of​ (a), (b), and​ (c)?

You are given the following probabilities in relation to two events, A and B: P(A)=0.4 PAB) -0.1. Determine the range of possible values of P(A/B). You are given the following data on a sample of 30 claim amounts: Sample mean = €470 Sample standard deviation - €630 One claim amount for €3,500 is considered to be an outlier. Calculate the revised sample mean and sample standard deviation if the outlier is removed from the data. [6]

Order Statistics: 11. (10 marks) An insurance claim amount following a car accident is described according to the following density function: f(y) = , y>1 y* 10 , otherwise a) (5 marks) Among n claim amounts you know E[Y]= 5What is n? b) (5 marks) Among n= 3 claim amounts, what is E[Y.,)?

Successful marketing proceeds the production of goods and services. Discuss.