00:01
It is given that for men sample mean is 23 .89, sample standard deviation is 4 .44, sample size is 1182 and for women sample mean x2 is 18 .03, sample standard deviation is 2, 4 .31 and sample size 1294.
00:37
So to find the standard error let us first find pooled standard deviation which is calculated using the formula n1 minus 1 s1 square plus n2 minus 1 s2 square divided by n1 plus n2 minus 2.
01:04
On substituting the values we will be getting 1182 minus 1 4 .44 square plus 1294 minus 1 4 .31 square divided by 1182 plus 1294 minus 2.
01:26
On simplifying we will be getting 4 .373 which is the pooled standard deviation.
01:31
To find the standard error, se is a product of pooled standard deviation with square root of 1 divided by n1 plus 1 divided by n2.
01:47
On substituting the values 4 .373 multiplied with square root of 1 divided by 1182 plus 1 divided by 1294.
01:58
On simplifying we will be getting 0 .176.
02:02
This is our standard error.
02:04
Then critical value for alpha 0 .02 and degree of freedom 2474 is 2 .328.
02:27
98 % confidence interval is calculated as x1 bar minus x2 bar minus t critical value multiplied with standard error.
02:39
X1 bar minus x2 bar plus t critical value multiplied with standard error.
02:51
On substituting the values 23 .89 minus 18 .03 minus 2 .328 multiplied with 0 .176.
03:03
23 .89 minus 18 .03 plus 2 .328 multiplied with 0 .176.
03:22
On simplifying we will be getting 5 .45 comma 6 .27...