00:01
Hello students, part a, the hypothesis is h naught p greater than or equal to 0 .1 versus alternative hypothesis h a p less than 0 .1.
00:15
Now given n is equal to 863 and p is equal to 0 .1, then we need to find the n into p that is equal to 0 .1 into 863 which is equal to 86 .3 and n into 1 minus p is equal to 776 .7.
00:55
Now since both are greater than 10, conditions are met.
01:11
Now test observed p that is p cap is equal to sample proportion p cap is equal to 47 divided by 863 that is equal to 0 .05446.
01:34
Now the test statistic is equal to z is equal to p cap minus p divided by square root of p into 1 minus p divided by n that is equal to 0 .05446 minus 0 .1 divided by square root of 0 .1 into 1 minus 0 .1 divided by 863.
02:15
So that is equal to minus 4 .46.
02:21
So p value is equal to probability that z less than minus 4 .46 is equal to 0.
02:35
Since p value is less than alpha that is equal to 0 .05, we reject the null hypothesis h naught.
02:58
So there is sufficient evidence to conclude p is less than 10 percentage.
03:16
Now the type 1 error means rejection of the true null hypothesis h naught and type 2 error means failure to reject the false null hypothesis that is h naught...