00:01
Hello students, we have given a random sample of 100 boards.
00:04
So, sample size n is equal to 100 and out of that 4 boards are defective.
00:11
That means x is equal to 4 and we have to test the hypothesis that more than 5 % of the circuit boards are defective.
00:21
So, this is we have to test at alpha is equal to 0 .10 level of significance.
00:27
So, to test the hypothesis first we will write the null hypothesis h naught as p is less than or equal to 0 .05 versus the alternative hypothesis that is h a as p is greater than 0 .05.
00:46
This is the claim.
00:48
Now to test this here first we need to calculate the sample proportion sample proportion proportion that is p hat which is equal to x divided by n which is equal to 4 upon 100 is equal to 0 .04.
01:12
Now here we will be using the one sample proportion test and for that the test statistic is given by z which is equal to p hat minus p divided by p into 1 minus p upon n and this whole term is inside the square root sign.
01:31
So, this is equal to 0 .04 minus 0 .05 upon 0 .05 into 1 minus p is 0 .95 divided by n is 100 and this is under the square root sign.
01:50
So, therefore, we will get the value of z is equal to minus 0 .46.
01:56
This is the required test statistic value...