Random samples of sizes n1 = 32 and n2 = 40 are to be drawn from two independent populations.
μ1 = 12.3 μ2 = 9.8
σ1 = 2.9 σ2 = 2.4
a.
,
; From standard normal distribution table
b.
; The Excel function is , =FDIST(1.3698,31,39)
Random samples of sizes n1 = 32 and n2 = 40 are to be drawn from two independent populations. M1 = 12.3 01 = 2.9 H2 = 9.8 02 = 2.4 a. P(X2 - X2 < 2) = b. P .PA>2)
Suppose we have taken independent, random samples of sizes n1 = 7 and n2 = 7 from two normally distributed populations having means μ1 and μ2, and suppose we obtain x1=240, x2=210, s1=5, and s2 = 6 Use critical values and p-values to test the null hypothesis H0: μ1 − μ2 ≤ 20 versus the alternative hypothesis Ha: μ1 − μ2 > 20 by setting α equal to .10. How much evidence is there that the difference between μ1 and...
The following information is obtained from two independent samples selected from two populations. n1=270 x¯1=5.98 σ1=1.11 n2=210 x¯2=5.40 σ2=2.47 Test at the 2% significance level if μ1 is greater than μ2 (one-tailed test). μ1 is Choose the answer from the menu in accordance to the question statement μ2 .
Please answer all parts, and show complete work.
6. (a) A finite population with N = 450 has a mean u = 112.5 and standard deviation o = 17.3. For samples of size n = 41, answer the following. The variance is for the sampling distribution of the sample mean X. (b) Random samples of sizes n1 = 32 and n2 = 40 are to be drawn from two independent populations. = 12.3 M1 01 = 2.9 M2 = 9.8...
Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1=51, n2=46, x¯1=57.8, x¯2=75.3, s1=5.2 s2=11 Find a 94.5% confidence interval for the difference μ1−μ2μ1−μ2 of the means, assuming equal population variances. Confidence Interval =
Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1= 37 n2=44 x-bar1= 58.6 x-bar2= 73.8 s1=5.4 s2=10.6 Find a 97% confidence interval for the difference μ1−μ2μ1−μ2 of the means, assuming equal population variances.
Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ21σ12 and σ22σ22 give sample variances of s12 = 100 and s22 = 20. (a) Test H0: σ21σ12 = σ22σ22 versus Ha: σ21σ12 ≠≠ σ22σ22 with αα = .05. What do you conclude? (Round your answers to F to the nearest whole number and F.025 to 2 decimal places.) F = F.025 = (Click to select)RejectDo...
Find the critical value to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that σ 2/1= σ2/2. Use α = 0.05. n1 = 15 n2 = 15 x1 = 25.74 x2 = 28.29 s1 = 2.9 s2 = 2.8
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that: a) x3 follows a gaussian distribution b) estimate mean value μ3 and variance σ3^2 c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)
Independent random samples of n = 100 observations each are drawn from normal populations. The parameters of these populations are: • Population 1: μ1 = 300 and σ1 = 60; • Population 2: μ2 = 290 and σ2 = 80. (1) What is the probability that the mean of Population 1 is between 294 and 306? (2) How many samples should be included if we want the probability in Part (1) to be at least 95%? (3) What is the...