Question

A random sample of 50 consumers taste tested a new snack food. Their responses were coded (0: do not like; 1: like, 2: indifferent) and recorded below: a. Test H0: p = 0.5 against Ha: p > 0.5, where p is the proportion of customers who do not like the snack food (n=17). Use α = 0.10. b. Find the observed significance level of your test.

Answer 1

The level of significance observed is 0.99154

Explanation:

Assuming that in a sample of size 50 people stated that they do not like the snack (p = 17/50), you have:

Proportion in the null hypothesis
`\pi_0=0.5`

Sample size
`n=50`

Sample proportion
`p=17/50=0.34`

The expression for the calculated statistic is:

`= ((p - \pi_0)√(n))/(√(\pi_0(1-\pi_0)))`

`= ((0.34 - 0.5)√(50))/(√(0.34(0.66))) = -2,38833`

The level of significance observed is obtained from the value of the statistic calculated:

`P(Z>Z_(calculated)) = 0.99154`