It is claimed that in a bushel of peaches, less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the p-value?
A) 0.0250
B) 0.4525
C) 0.0475
D) 0.0500

Question

Quizplus · Accepted Answer

Since the null hypothesis states that less than 10% (0.10) of peaches are defective, we can use a one-tailed test with the alternative hypothesis being that more than 10% are defective.

To calculate the p-value, we can use the normal approximation to the binomial distribution with a mean of (0.10)(400) = 40 and a standard deviation of sqrt[(0.10)(0.90)(400)] = 6. Therefore, the z-score is (50-40)/6 = 1.67.

Looking at a standard normal distribution table, we find that the area to the right of 1.67 is 0.0475. This means that the probability of observing a sample with 50 or more defective peaches, assuming that the true proportion of defective peaches is less than 10%, is 0.0475. This is the p-value.

Since the p-value (0.0475) is less than the significance level (0.05), we reject the null hypothesis and conclude that there is evidence to suggest that more than 10% of peaches are defective.

It Is Claimed That in a Bushel of Peaches, Less