Question

A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling. survey a simple random sample of 300 voters in the state. The team decides to use a significance level of 0.05 when testing their hypothesis.

The data given was 175 yes responses and 125 no responses

1. Choose the appropriate hypotheses:

Ho: p<0.55

Ha: p>0.55

Ho: p>0.55

Ha: p<0.55

Ho: p≥0.55

Ha: p<0.55

Ho: p≤0.55

Ha: p>0.55

round to 3 decimal places for each of these

2. What is the appropriate test statistic?

3. What is the critical value, z?

4. What is the p-value for the test?

5. How big can the proportion be before the researchers will reject the null hypothesis? (critical pbar)

Answer 1

Solution :

This is theright tailed test .

The null and alternative hypothesis is

H₀ : p =0.55

H_a : p > 0.55

= x / n = 175 / 300 = 0.5833

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5833 - 0.55 / [(0.55 *0.45) / 300]

= 1.16

Critical value = 1.645

P-value = 0.1229

Fail to reject the null hypothesis .