Question

A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty. With a significance level of 1% can the statement made by the company be accepted?

Answer 1

The population proportion P = 6% = 0.06 

The null hypothesis: H₀ : P ≤ 0.06 

Alternative hypothesis: H₁ : P > 0.06 

For α = 1% = 0.01. Z_α = 2.33

The test statistic is P + 2.33 (√(0.06)(0.094)/300) = 0.092 (where n = 300, P = 0.06, Q = 0.94) 

Since the calculated value is less than the table value, 0.092 < 2.33,we accept the null hypothesis H₀ . 

Hence the statement of the company can be accepted.