Question

A study claims 32% of U.S. adults eat chocolate daily. A researcher suspects the actual percentage is greater than this. The researcher randomly selects 88 people and finds 39 of them eat chocolate daily. Perform a hypothesis test using ∝ = 0.05. Step #1: State the null and alternative hypothesis. Identify the claim.Step#2: Find the test value.Which test is needed?Right,left, or two tailed Step #3: Find the p-value. Do not reject or reject the null hypothesis?

Answer 1

Solution :

Given that,

= 0.32

1 - = 0.68

n = 88

x = 39

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.44

This a right (One) tailed test.

Step #1:

The null and alternative hypothesis is,

Ho: p = 0.32

Ha: p 0.32

Step #2:

Test statistics

z = ( - ) / *(1-) / n

= ( 0.44 - 0.32) / (0.32*0.68) /88

= 2.413

The null and alternative hypothesis is,

Step #3:

P-value = P(Z > z )

= 1 - P(Z < 2.413 )

= 1 - 0.9921

= 0.0079

The p-value is p = 0.0079, and since p = 0.0079 < 0.05, it is concluded that the null hypothesis is rejected.

Step #4:

Reject the null hypothesis.