00:02
Hello students, the given information is x equal to 50, n equal to 200.
00:13
It implies p hat equal to x upon n.
00:18
We get value of p hat as 0 .25.
00:23
Then to test h0, p equal to 0 .20 versus h1, p is not equal to, p is greater than 0 .20.
00:43
Then test statistics, for this test it is given as z equal to p hat minus p upon under root of p into 1 minus p upon n.
01:02
All values are already given.
01:04
Then just put the values here, we get the value of z as 25.
01:09
And corresponding p value is less than 0 .00001.
01:18
And we have to find here p value, then the correct option is e, below 0 .001.
01:30
Now second question given is p equal to 0 .43, n equal to 16, x equal to 35.
01:48
Then again p hat is equal to x upon n.
01:53
And by simplifying we get value of p hat as 0 .5883.
02:08
Here we have to find the values of mean and standard deviation, related with this information.
02:17
Then mean of p hat is equal to mu of p hat is given as capital p.
02:30
And value of p is already known, which is 0 .43.
02:36
Now standard deviation of p hat is equal to sigma of p hat, it is denoted by sigma of p hat.
02:45
And it is given as p into 1 minus p upon, after simplifying we get this value as 0 .064...