00:01
Hello everyone, so this is the question that we have.
00:02
We have a research department of new hampshire insurance.
00:08
So a random sample of 400 people were taken that revealed 120 had at least one accident in the previous three year period in three year period.
00:36
Similarly, a sample of 600 policies were taken.
00:45
Now, on married people, this was for married people, and which revealed 150 had met with an accident.
01:02
So at 0 .05 significance level, we need to tell that what is the difference in proportions of people having accidents of people having accidents? now, to be better concise way, we need to tell the pool proportion, part one, part two, we need to tell the decision rule.
01:50
Decision rule to reject part three we need to test the we need to find the test statistic which is said part four of the question we need to find the p value part five we need to tell our decision regarding edge not so let's jump on to the solution of the question now part one first let's write down so the first sample n1 is 400.
02:27
Its probability 120 met with an accident out of 400, it's going to be 0 .3.
02:35
Second sample, n2 is of 600.
02:39
Probability, p2 is 150 met with an accident over 600, that is 0 .4.
02:47
And alpha level of significance is 0 .05.
02:51
0 .0 .05.
02:55
Now, if we take this data, if we take the null hypothesis h0, which is p1 minus p2 is equal to 0, an alternate hypothesis h of a, which is p1 minus p2, not equal to 0.
03:11
So, for the first part, we give the probability as p1n1, plus p2 n2 divided by n1 plus n2 so this is going to be put in all the values so 0 .3 multiplied by n1 is 400 plus p2 is 0 .4 multiplied by 600 divided by 400 plus 400 plus 400 plus 600 that is going to be equal to 0 .36 now part two of the question we have the intervals given by the z score table from minus z alpha divided by 2 to z alpha divided by 2.
04:04
By the formula, which is nothing but z alpha divided by 2, in this case is going to be from minus 1 .96 to 1 .96 using the z score table...