Question

step 2: find the margin of error used in constructing the confidence interval. round your answer to six decimal place.

step 3 construct 99% confidence intervel. round to 6 decimal place

Given two independent random samples with the following results: N = 16 Xi = 193 X2 = 173 $ = 31 Use this data to find the 99% confidence interval for the true difference between the population means. Assume that the population variances are $2 = 22 equal and that the two populations are normally distributed. Copy Data Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Tables Keypad Keyboard Shortcuts Next Answer/How to Enter) 1 Point V

Step 2 find the critical value in constructing confidence intervel.

step 3 find the standard deviation

Step 4construct 90% confidence interval

Answer 1

1.

The point estimate is $\bar{x_1} - \bar{x_2}= 193 - 173 = 20$

Here, 21 = 193.000, 81 = 31.000, n1 = 16,22 = 173.000, S2 = 22.000, n2 = 9 and associated degrees of freedom df=nn2 -2 = 16+9 -2 =23 and pooled variance (n1 - 1)s +(n2 - 1)s ni + n2 - 2 795.086957 and pooled standard error Sp = V s = 795.086957 = 28.197286 and standard error for the difference between means 1 1 SEN 1 ni + 795.086957* 1 V 16 + 331.286232 n2 9 At 99 percent level of confidence, the margin of error is 1 1 ME=t109,90 + Sp* ,7, +1 ni n2 1 1 =t0.005,23 * 28.1973* + V 16 9 = 2.807336 * 28.1973 * 1 V 16 + 1 9 32.983020 a 99 percent confidence interval for the differnce in population means (M1 - 12 ) is 1 1 = 1 -12 +8p1 PV ni + *t 10.990 ,23 n2 = 21-22 ME (193.000 - 173.000) = 32.983020 = 20.000 + 32.983020 = (-12.983020,52.983020) (-12.98,52.98)

2.

Let à denotes the sample mean of difference, s denotes the sample standard deviation of difference and n denotes the sample size. Here, Sd 0.7143 à = -1.756, să 0.5103, sd = 0.7143, n = 9, standard error of mean = 0.238112 vn ✓g = The margin of error is Sd ME *t 1-0.9 0.7143 ✓9 * t0.05,8 ✓n 0.7143 * 1.859548 = 0.442782 0.443 ✓9 ,8 2 a 90 percent confidence interval for the population mean of difference ud is Sd = d + *t 1-0.9 vn ,8 0.714 =-1.756 + * 10.05,8 ✓9 0.714 = -1.756 + * 1.859548 V9 = -1.756 + 0.442782 = (-2.198337, -1.312774) ~(-2.20, -1.31)

The critical value in constructing confidence intervel is $t_{critical} = t_{\frac{1-0.9}{2}, 8} = t_{0.05,8} =1.859548$