Question

The Field Poll and UC Berkeley’s Institute of Government Studies conducted a poll of a

random sample of 500 likely voters residing in California. 57% of those surveyed were in

favor of legalizing marijuana. The pollsters were concerned whether the percentage of the

population in favor of legalization formed a majority. So, their question was the following:

Does support for marijuana legalization among California likely voters differ from 50%?

1. Provide the null and alternative hypotheses in both sentences and notation.
2. Calculate the Z test statistic for the hypothesis test.
3. Identify the associated p‐value for your test statistic.
4. Using an alpha of 0.01, state your conclusion in reference to the null hypothesis.
5. Interpret your result in reference to the alternative hypothesis.

Answer 1

The null and alternative hypothesis

H0: p = 0.50

Ha: p 0.50

Test statistics

z = ( - p) / sqrt(p(1-p) / n)

= ( 0.57 - 0.50) / Sqrt ( 0.50 * 0.50 / 500)

= 0.99

p-value = 2 * P(Z > z)

= 2 * P(Z > 0.99)

= 2 * 0.1611

= 0.3222

Since p-value > 0.01 level, We fail to reject H0.

We conclude at 0.01 level that we do not have sufficient evidence to support the claim that proportion

is different from 50%