Answer:
Less than 4% of a company's widgets are defective.
Step-by-step explanation:
In this case we want to be reasonably certain that less than 4% of a company's widgets are defective.
The significance level of the test is, α = 0.01.
The hypothesis can be defined as follows:
H₀: At least 4% of a company's widgets are defective, i.e. p ≥ 0.04.
Hₐ: Less than 4% of a company's widgets are defective, i.e. p < 0.04.
The information provided is:
n = 250
x = 6
The sample proportion is,
Compute the test statistic value as follows:
The test statistic value is -1.29.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
So,
p-value = 0.0985 > α = 0.01.
The null hypothesis will not be rejected at 1% significance level.
Thus, there is not enough evidence to support the claim.
Conclusion:
Less than 4% of a company's widgets are defective.