12 marks Let independent random samples of sizes n and n2 be taken respectively from two normal distributions with unkn...
Consider independent random samples of size n, and n, from respective normal distributions, Xi ~ Nuh, σ ) and Y, ~ Num σ ). 30 (a) Derive the GLR test of Ho : σ|-σ1 against H. σ. σ1, assuming that and μ2 are known. (b) Rework (a) assuming that andHa are unknown. Consider independent random samples of size n, and n, from respective normal distributions, Xi ~ Nuh, σ ) and Y, ~ Num σ ). 30 (a) Derive the...
Let independent random samples, each of size n, be taken from the k normal distributions with means u cd [j - (k 1)/2], j = 1, 2,..., k, respectively, and common variance o2. Find the maximum likelihood estimators of c and d
From two normal population assumed to have the same variance, independent random samples of sizes 15 and 19 were drawn. The first sample (n1=15) yielded mean and standard deviation 111.6 and 9.5 respectively, while the second sample (n2=19) gave mean and standard deviation 100.9 and 11.5 respectively. Suppose Ho: mu1 = mu2 Ha: mu1 > mu2 (alpha level = 0.05) (i) Write the rule for rejecting Ho in terms of T-scores. (ii) Compute the T statistic, a p-value for the...
From two normal population assumed to have the same variance, independent random samples of sizes 15 and 19 were drawn. The first sample (n1=15) yielded mean and standard deviation 111.6 and 9.5 respectively, while the second sample (n2=19) gave mean and standard deviation 100.9 and 11.5 respectively. Suppose Ho: mu1 = mu2 Ha: mu1 > mu2 (alpha level = 0.05) (i) Write the rule for rejecting Ho in terms of T-scores. (ii) Compute the T statistic, a p-value for the...
2b) The random samples with sizes 14 = 16 and n2 = 25 respectively were taken from two normal populations. The variances for both samples were s2 = 48 and s= 26 respectively. Using an appropriate hypothesis, carry out a test to determine whether the variance from the first population is higher than the variance from the second population. Use a = 0.05.
1) Consider two independent random samples of sizes n1 = 14 and n2 = 14, taken from two normally distributed populations. The sample standard deviations are calculated to be s1= 1.98 and s2 = 5.71, and the sample means are x¯1=-10.2and x¯2=-2.34, respectively. Using this information, test the null hypothesis H0:μ1=μ2against the one-sided alternative HA:μ1<μ2, using Welch's 2-sample t Procedure for independent samples. a) Calculate the value for the t test statistic. Round your response to at least 2 decimal...
Suppose that independent samples of sizes n1, n2, . . . , nk are taken from each of k normally distributed populations with means μ1,μ2, . . . , μk and common variances, all equal to σ 2. Let Yi j denote the j th observation from population i, for j = 1, 2, . . . , ni and i = 1, 2, . . . , k, and let n = n1 + n2 + ··· + nk...
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 =
Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right. a. Assuming equal variances, conduct the test Ho ??-?2):0 against Ha : (??-?2)#0 using ?:010. b. Find and interpret the 90% confidence interval for ( 1- 2)- Sample 1 Sample 2 n1 18 n2 13 x1-5.2 x27.7 s1 3.7 s2 4.3 a. Find the test statistic. The test statistic is (Round to two decimal places as needed.)
Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right. a) Assuming equal variances, conduct the test Ho: (u1-u2)=0 against Ha: (u1-u2)=/=0 using a=0.05 b) Find and interpret the 95% confidence interval for (u1-u2) Sample1: n1=17, x1=5.9, s1=3.8 Sample2: n2=10, x1=7.3, s2=4.8