00:01
Hello student, in the given question, to answer this question we need to conduct a hypothesis test.
00:07
So, the null hypothesis is that the proportion of defective peaches is less than or equal to 0 .10 versus the alternative hypothesis is that the proportion of defective peaches is greater than 0 .10.
00:34
We can use the normal approximation to the binomial distribution to test this hypothesis.
00:42
Use normal approximation to the binomial distribution to test this hypothesis.
01:11
So, the test statistic is given as z is equal to p cap minus p upon square root of p into 1 minus p upon n, where p cap is the sample proportion, p is the hypothesized proportion under the null hypothesis, small n is the sample size, the p value of probability of observing this statistic is extremely or more extremely than 1 observed.
01:43
So, assuming the null hypothesis is true.
01:46
Now, substituting the given value p cap is equal to 50 upon 400 which is equal to 0 .125.
01:57
The value given for p is 0 .10 and n is 400.
02:06
So, substituting all this value in the z formula, we get z is equal to 0 .125 minus 0 .10 upon square root of 0 .10 multiplied by 0 .90 upon 400 which is equal to 1 .76.
02:34
Using standard normal distribution table or a calculator, we find out the probability of z is greater than 1 .76 is approximately equals to 0 .039 and since given value alpha is equal to 0 .025, this p value is greater than, here p value is greater than the alpha value...