00:01
In this question, we have been given that the value of p0 will be here 0 .50 and it is the hypothesized population proportion.
00:09
Now the value of x that is favorable cases will be 147.
00:13
Therefore, the value of sample size is here 350.
00:16
So, now we can say that the value of p hat will be here equals to it is x divided by n and it will be here 0 .42.
00:26
So, now we can say that alpha value will be 0 .05 and hence the value of null hypothesis can be here written such that it is here p and that is equals to 0 .50 versus the alternate hypothesis which can be here written that p is not equals to 0 .50.
00:45
So, we are dealing with a two tailed test because here in the alternate hypothesis we are having the symbol of not equals to.
00:53
So, here we are performing z test as well.
00:56
So, it can be written like this and then we can say that the value of rejection reason can be here written based on the given information that z critical is going to be 1 .96 for the alpha value of 0 .05.
01:12
So, from here we can say that the rejection reason r will be here equals to z such that it is here modulus of z and that is greater than 1 .96 and then we can say that the value of z that is test statistic or we can say z statistic will be here p hat minus it is here p naught divided by it is here going to be under root of we can say it will be p naught multiplied with 1 minus p naught and now in the denominator it is n.
01:42
So, this very value will be here 0 .42 minus it is here 0 .50 and then in the denominator it is going to be under root of let us write it will be 0 .50 and then here it is 1 minus 0 .50...