Part II: Confidence Intervals for comparison of differences a. For the Real GDP

Question

Part II: Confidence Intervals for comparison of differences a. For the Real GDP data presented in the Raw Data set (re: MS Excel file), use the formula for the difference between two means of two independent samples to compare the following two timeframes: 1920 to 1939 and 1930 to 1949. Show all work for full or partial credit. Assume alpha, , is 0.05. I b. Given the confidence interval computed in part 'a', is there enough evidence to suggest that the two means (real GDP for 1920 to 1939 and 1930 to 1949) are different? (5 points) C. Explain with elaboration your response to part ‘b'.

Explanation / Answer

mean1=1.123 and mean2=1.317

now we find the Standard error for difference of two sample means

((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

(1-alpha)*100% confidence interval for population mean difference =

=sample mean difference±t(alpha/2,n)*SE(difference)

95% confidence interval =0.194±t(0.05/2, 38)*0.4042=0.194±2.02*0.4042=0.194±0.816=(-0.610, 01.001)

so mean1 is not significantly different from mean2

If a 95% confidence interval includes the 0, then there is no statistically meaningful or statistically significant difference between the groups.

sample mean s s2 n (n-1)s2 sample1 1.123 0.26 0.0676 73 4.8672 sample2 1.317 0.509 0.259081 73 18.653832 difference= 0.194 0.326681 146 23.521032 sp2= 0.1633405 sp= 0.404154055

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