It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the critical value for α = 0.025?
A) +1.960
B) ±1.645
C) -1.960
D) -1.645

Question

Quizplus · Accepted Answer

To find the critical value for α = 0.025, we need to use a Z-table. Since the sample size is greater than 30, we can use the normal distribution. 
First, we need to find the sample proportion of defective peaches: 
p̂ = 50/400 = 0.125
Next, we can calculate the standard error of the sample proportion: 
SE = sqrt(p̂(1-p̂)/n) = sqrt(0.125(1-0.125)/400) = 0.0221
Using the Z-table or calculator, we can find the critical value for α = 0.025 to be -1.960. 
Therefore, the answer is C.

It Is Claimed That in a Bushel of Peaches, Less