00:01
To solve this question, first of all we will let here x1, x2 and so on till xb, b are random sample.
00:24
And sample sizes here n is a from the poison distribution.
00:37
So now our parameter here will be as lambda.
00:46
So as example our x -i will be for the poison of lambda parameter and then we can find our probability for the event x is equal to small x which will be as when x is equal to 0 1 2 and so on we will get our value e to the power of minus lambda lambda to the power of x divided by factorial x and otherwise it will be equal to 0.
01:28
So now here we will reject our null hypothesis which is lambda is equal to 0 .5 if the observed observed sum as submission of i is equal to 1 to p for x i is greater than not equal to 8.
02:00
So now we will find here our critical region that will be as x such that summation of i is equal to 1 to 8 of x i greater than or equal to 8 and according to the additive property as per additive property of poison distribution we have our value for submission of i is equal to 1.
02:51
1 to 8 as our sample size is 8 here x i submit p 8 lambda and now we will let here u is equal to submission of i is equal to 1 to 8 x i let's say thus and under our null hypothesis is ho when ho is true.
03:26
If ho is true then we can write here u is equal to submission of i is equal to 1 to 8 x i similar to p 8 in the bracket 0 .5 so now we can see u is for poison of you and now the critical reason here as for the question our critical reason is u is greater than or equal to 8 and therefore we can say to find lambda now to find lambda our alpha will be able to p type to error and therefore p we will reject null hypothesis when when h -o is true and therefore we can write here p u is greater than or equal to 8 slash lambda is equal to 0 .5 so therefore we get u similar to poison of you and therefore our value for alpha will be equal to 1 minus probability of getting u less than 8 so that that is 1 minus probability of getting u less than or equal to 7 and this event can be finded by probability of getting u is equal to 0 added by probability of getting u is equal to 1 further till probability of getting u is equal to 7 you you have to compute all these event here and the events will be equal to 1 minus e to the power of minus 4 4 to the power of 7 divided by factorial 0 added by e to the power of minus 4, 4 to the power of 1 divided by factorial 1 added by e to the power of minus 4 4 to the power of 2 divided by factorial 2 and so on till the 7 term which is e to the power of minus 4 4 to the power of 7 divided by factorial 7.
06:14
So this can be calculated further as 1 minus minus within the bracket we can take e to the power of minus 4 common here.
06:26
So it will be e to the power of minus 4 within the bracket when we saw this will be 1 plus 4 plus 16 by 2, 32 by 3 plus 32 by 3 plus 128 by 15 plus 256 divided by 455...