00:01
Hello students, here the sample size n is equal to 1500.
00:05
Then also we have given that 40 % of them have a high definition television.
00:10
That means we have given the value of p hat which is equal to 0 .47.
00:17
And then also we have given the significance level that is alpha is equal to 0 .01.
00:22
And at this level of significance, we have to test the claim that fewer than half of all households have a high definition television.
00:32
So therefore, we can write the null hypothesis h naught as p is equal to 0 .5 versus the alternative hypothesis h a as p is less than 0 .5.
00:45
So this is we have to test.
00:47
Now we have the value of p hat and n and the test is left tailed as in the alternative hypothesis we have p is less than 0 .5.
00:58
So it is a left tailed test left tailed test.
01:07
So therefore, the test statistic is given by z which is equal to p hat minus p naught divided by p naught into 1 minus p naught upon n and this whole term is inside the square root sign...