Independent random samples selected from two normal populations
produced the sample means and standard deviations shown
below:
Sample 1 |
Sample 2 |
---|---|
x̅1 = 5.4 |
x̅2 = 8.2 |
s1 = 5.6 |
s2 = 8.2 |
n1 = 20 |
n2 = 18 |
Conduct the test H0 : μ1
- μ2 = 0 against
H1 : μ1 -
μ2 ≠ 0 ,then the test statistic is
__________.
Solution:
To test the hypothesis, H0 : μ1 - μ2 = 0 against H1 : μ1 - μ2 ≠ 0
Assuming equal variances , we perform t test for the difference between two means.
Let be the the pooled variance.
=
The test statistic t is given by
t =
=
=
= -1.240
The test statistic is -1.240
Independent random samples selected from two normal populations produced the sample means and standard deviations shown...
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
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.
Independent random samples were selected from two quantitative populations, with sample sizes, means, and standard deviations given below. n1 = n2 = 60 x1 = 125.3 x2 = 123.4 s1 = 5.7 s2 = 6.1 a) Construct a 95% confidence interval for the difference in the population means (μ1 − μ2). (Round your answers to two decimal places.) to b) Find a point estimate for the difference in the population means. c) Calculate the margin of error. (Round your answer...
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 (H1-H2) = 0 against Hy: (H1-H2) #0 using a = 0.10. b. Find and interpret the 90% confidence interval for (H1-H2) Sample 1 Sample 2 ny - 18 ng - 11 X2 7.8 X = 5.6 Sy = 3.1 82 4.7 a. Find the test statistic, The test statistic is (Round to two...
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 dev atons shown to the right. a. Assuming equal variances, conduct the test Ho: (μι-μ2)-U against Ha: μι-μ2) #0 using α .10. b. Find and interpret the 90% confidence interval for(μ1-μ2) Sample 1 Sample 2 x1 59 x2-7.9 13 2-4.8 a. Find the trst statistic. The test statistic is Round to two decimal places as needed.) ind the p vaue. The p-value is Round to three...
Independent random samples were selected from two quantitative populations, with sample sizes, means, and standard deviations given below. n1= 55, n2= 65, xbar1= 35.5, xbar2= 31.4, s1= 5.7, s2= 3.3 1.) Construct a 95% confidence interval for the difference in the population means (mu1- mu2). (Round your answers to two decimal places) 2.) Find a point estimate for the fifference in the population means. 3.) Calculate a margin of error. (Round your answer to two decimal places)
9.2.12-T Independent random samples selected from two normal populations produced the sample moans and standard deviations shown to the right. a. Assuming equal variances, conduct the test Ho: (4-1) = 0 against H: (1 ) using a = 0.05. b. Find and interpret the 95% confidence interval for (1-2) Sample 1 Sample 2 ng = 1802-11 Xy = 5.1 X2 = 7.9 -3.2 Sy = 4.9 a. Find the test statistic The test statistics - 1.87. (Round to two decimal...
Two samples are taken with the following sample means, sizes, and standard deviations ¯x1 = 32 ¯x2 = 35 n1 = 68 n2= 56 s1 = 3 s2= 4 Estimate the difference in population means using a 96% confidence level. Use a calculator, and do NOT pool the sample variances. Round answers to the nearest hundredth. < μ1−μ2 <