Question

In a recent survey, 72 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries. If there is no difference in the proportions who prefer each type in the population, the chance of such extreme results in a sample of this size is about .03. Because .03 is less than .05, we can conclude that there is a statistically significant difference in preference. Give a numerical value for each of the following.

(a) The p-value.
(b) The level of significance, α.
(c) The sample proportion.
(d) The sample size.
(e) The null value.

Answer 1

a) P=0.03

b) α=0.05

c) 0.72

d) 100

e) 0.72

Explanation:

a) The P-value is the probability of the sample result. In this case the P-value is 0.03.

b) The level of significance is the threshold of probabilty for the null hypothesis to be reejcted or not. It is contrasted with the P-value to know if the effect is significant. In this case, the level of significance is 0.05.

NOTE: if it is a two-side test, the level of significance is 0.1 (two times 0.05).

c) The sample proportion is the one that results from the sample data. In this case, the sample proportion is 0.72.

`p=72/100=0.72`

d) The sample size is the amount of consumers reported. In this case is 100 customers.

e) The null value is 0.72 (equal to the sample proportion), because it is tested if there is no difference between the population proportion and the sample proportion.