00:01
Hello students for the sub part a they given that n is equal to 130 and p is equal to 25 percentage which is 0 .25.
00:13
Now here we need to find the margin of error of this poll that is the conference interval given as 95 percentage so alpha is equal to 0 .05.
00:25
Now the formula for calculating the margin of error is here the n is greater than 30 so here is that alpha by 2 into square root of p into 1 minus p by n to calculate the critical value is at alpha by 2 which is at 0 .05 by 2 we get 1 .96 now substitute the known values in the formula of margin of error we get 1 .96 into 0 .25 into 1 minus 0 .25 divided by 1 .5 by simplifying all these values, we get 0 .074.
01:11
This is our margin of error.
01:13
Then for the subpart b, they given that n is equal to 15 and mean x bar is equal to 30 and the standard deviation yes is equal to n to find the margin of confidence interval as 90 percentage.
01:39
So alpha is equal to 0 .10.
01:45
Now here the sample size is less than 30, so use t critical value, that is the formula for calculating the margin of error is t alpha by 2 into s divided by square root of n.
02:00
So calculate that critical value t alpha by 2 n minus 1, which is t 0 .10 by 2, 14 degrees of freedom, we get 1 .761.
02:13
Now substitute the known values we get our margin of error...