00:01
So, given that x bar for part 4 is equal to 14 .7, then we have the standard deviation s is equal to 0 .7, number of observations is equal to 11, confidence interval is equal to 95 percent and degree of freedom denoted by df is equal to 11 minus 1 which is equal to 10.
00:27
Therefore, at standard error is equal to s divided by root over n which is equal to 0 .7 divided by root over 11 which is equal to 0 .211.
00:52
Then we have at 95 percent level of significance or confidence interval, the value of t is 1 minus 95 percent which is equal to 1 minus 0 .95 which is equal to 0 .05.
01:15
Therefore, alpha by 2 is equal to 0 .025.
01:19
Hence, tc or critical region is equal to t 0 .025, 10 which is according to the t table is 2 .228.
01:29
Now, margin of error is equal to t alpha by 2 comma degrees of freedom entire thing multiplied with standard error.
01:52
This is equal to 2 .228 multiplied with 0 .2111 which is equal to 0 .4703.
02:03
Therefore, the lower limit is equal to x bar minus error which is equal to 14 .7 minus 0 .47 which is equal to 14 .230 and upper limit is equal to x bar plus error which is equal to 14 .7 plus 0 .47 which is equal to 15 .170.
02:40
These are the lower and the upper limits.
02:45
For part 5, we have sigma or variance of population is 9, error is equal to 3 and confidence interval percentage is equal to 98 and 98 percent confidence interval we have alpha is equal to 1 minus 98 percent which is equal to 1 minus 0 .98 which is equal to 0 .02 and alpha by 2 is equal to 0 .01.
03:21
Therefore, z alpha by 2 is equal to 2 .3.
03:27
Therefore, sample size is equal to 10 which is equal to z multiplied with sigma divided by error whole thing squared...