How productive are employees? One way to answer this...

How productive are employees? One way to answer this question is to study annual company profits per employee. Let x1 represent annual profits per employee in computer stores in St. Louis. A random sample of n1 = 11 computer stores had a sample mean of x?1 = 25.2 thousand dollars profit per employee with a sample standard deviation of s1 = 8.4 thousand dollars. Another random sample of n2 = 9 building supply stores in St. Louis had a sample mean of x?2 = 19.9 thousand dollars per employee with a sample standard deviation of s2 = 7.6 thousand dollars. Does this indicate that in St. Louis, computer stores tend to have higher mean profits per employee than building supply stores? Use ? = 0.01.

Transcript

00:01 Here we will be setting our null hypothesis at h0 is to mu1 minus mu2 is equal to 0.

00:08 And our alternative hypothesis will be setting at h1 is to mu1 is here mu1 minus mu2 is greater than 0 which can be rewritten as here h1 is to mu1 is greater than mu2.

00:28 Here mu1 is our composure stores for population 1 and mu2 is here our building stores for population 2.

00:39 Now here our given null hypothesis is 0 .01 and our sample for population 1 our sample mean is given here 25 .2 and for population 2 our sample mean is given 19 .9.

01:04 Our sample size is given n1 is equal to 11 and for population 2 it is given 9 our standard deviation s1 is equal to given 8 .4 and for population 2 it is given 7 .6 now we'll find out here our pooled variance that is sp is equal to so, sb2 is equal to n1 minus 1 into s1 squared plus n2 minus 1 into s2 squared by here in the denominator n1 plus n2 minus 2.

01:44 Now, we put our respective values here.

01:46 So our value of n1 is 11 minus 1 into our s1 value is 8 .4 n square plus our n2 value is 9 minus 1 into s2 square.

02:00 Our s2 value is given 7 .6 and we need it square by in the denominator our value of n1 which is 11 plus our value of n2 which is 9 minus 2.

02:13 So, on solving, we will be getting our pooled variance value here.

02:19 Our pooled variance will be 64 .87.

02:25 Now, here we will find out our test statistics.

02:30 Our test statistics formula will be here.

02:33 Our test static formula is x1 minus x2 bar x1 bar minus x2 bar by in the denominator square root of our pooled variance square by n1 plus our pooled variance sp square by n2...

Question

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