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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.

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aramisdegaula1977

Answer:

The level of significance observed is 0.99154

Step-by-step 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 [tex]\pi_0=0.5[/tex]

Sample size [tex]n=50[/tex]

Sample proportion [tex]p=17/50=0.34[/tex]

The expression for the calculated statistic is:

[tex] = \frac{(p - \pi_0)\sqrt{n}}{\sqrt{\pi_0(1-\pi_0)}}[/tex]

[tex]= \frac{(0.34 - 0.5)\sqrt{50}}{\sqrt{0.34(0.66)}} = -2,38833[/tex]

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

[tex]P(Z>Z_{calculated}) = 0.99154[/tex]

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