Question

A company in the food industry stores a large number of canned goods in a central warehouse. Last year, 3% of the canned goods had damage (for example, ugly worms or dents in the can), and the warehouse manager suspects it could be even worse this year.

To investigate this, we randomly selected 260 of the preserves and of these, 13 have
damage.
(a) Conduct hypothesis testing to test if the warehouse manager's suspicions can be considered where
Acknowledged.
(b) Formulate an interpretation of the P-value for the test in the (a) assignment. (The P value is
probability of ...)
(c) If we did the investigation, how could we do it to get higher?
strength of the test in the (a) assignment? Justify the answer.
(d) Describe what a Type I error and a Type II error would mean in this context.

Answer 1

Given,

p0 = 0.03

Sample proportion, p = 13/260 = 0.05

Number of samples = 260

(a) the hypothesis is,

Null hypothesis, H0 : p ≤ p0

​​​​​​The number of canned goods gone bad is equal to or lesser than last year

Alternate Hypothesis, Ha : p > p0

The number of canned goods gone bad is greater than last year

(b)

We know that,

z = 1.89

The p value is,

p = 0.03

Assuming the level of significance, a = 0.05,we reject the null hypothesis. Since p < a(0.3 < 0.05).

Therefore, the number of canned goods gone bad is greater than last year.

(c) to increase the strength of the test

1. Increase the sample size
2. Increase the level of significance

(d)

Type I error : Incorrectly rejecting a true null hypothesis causes a type I error. Which means rejecting the null hypothesis that the number of canned goods gone bad is less or equal to last year.

Type II error : Failing to reject a false null hypothesis causes type II error. Which means failing to reject the null hypothesis when the number of canned goods gone bad is greater than last year.