Question

a) Suppose the first sample of 100 observations is selected from a population with mean 150 and vanance = 1580 Construct an interval extending 2 standard devi ati ons ola on eac h side of μ1 = 150 and b) Suppose the second sample of 100 observations is selected from a population with mean variance σ = 1180 Construct an interval extending 2 standard deviations of z2 on each side of μ2. c) Consider the difference between the two sample means ( -T2) Compute the mean and the standard deviation of the sampling distribution of ( Mean Standard Deviation = d) Based on 100 obs ervations, construct an interval extending 2 standard deviations of ()on each side of

Please explain how you got the answer. Thank you!

Answer 1

Excel add-in (Mega Stat) procedure Step 1: In EXCEL, Select Add-Ins> Mega Stat> Confidence intervals/Sample size. Step 2: Choose Confidence intervals-Mean Step 3: Enter 150 as the mean, 40 as the Std. Dev, and 100 as the n Step 4: Choose z Step 4: In Confidence Level. Choose 95% Step 5: Click Preview and then OK. Excel add-in (Mega Stat) output Confidence interval mean 95% confidence level 150 mean 40 std. dev 100 n 1.960 z 7.840 half-width 157.840 upper confidence limit 142.160 lower confidence limit Thus the confidence interval is 142.163 M s157.84

Excel add-in (Mega Stat) procedure: Step 1: In EXCEL, Select Add-Ins > Mega Stat > Confidence intervals/Sample size Step 2: Choose Confidence intervals-Mean. Step 3: Enter 150 as the mean, 34 as the Std. Dev, and 100 as the n. Step 4: Choose z. Step 4: In Confidence Level. Choose 95%. Step 5: Click Preview and then Ok. Excel add-in (Mega Stat) output: Confidence interval mean 95% confidence level 150 mean 34 std. dev 100 n 1.960 z 6.664 half-width 156.664 upper confidence limit 143.336 lower confidence limit

Thus the confidence interval is 143.336 156.664 Mean H -150 150 -1580+1180 2760 52.5357 Excel add-in (Mega Stat) procedure:

Step 1: In EXCEL, Select Add-Ins> Mega Stat> Hypothesis Tests. Step 2: Choose Compare Two Independent Groups Step 3: Choose Summary Input. Step 4: In Group 1, enter B1:B4 (Select ranges with label mean, SD, n). Step 5: In Group 2, enter D1:D4 (Select ranges with label mean, SD, n). Step 6: Enter 0 Under Hypothesized difference. Step 7: Check z-test, enter Confidence level as 95.0 Step 8: Choose not equal in alternative. Step 9: Click OK. Excel add-in (Mega Stat) output:

Hypothesis Test: Independent Groups (z-test) Sample 1 Sample 2 150 150 mearn 34 std. dev 100 100 n 0.000 difference (Sample 1 Sample 2) 5.250 standard error of difference 0 hypothesized difference 0.00 z 1.0000 p-value (two-tailed) 10.289 confidence interval 95% lower 10.289 confidence interval 95% upper 10.289 margin of error Thus the confidence interval is-10.289 (H 10.289