Question

70% of voters in a certain state support an increase in the minimum wage. A researcher believes that the percentage of fast food workers who support this is higher than 70%. In a random sample of 300 fast food workers, 240 support an increased minimum wage. Testing at a significance level a=.05

find:  

a. H_0, H_a

b. p̂

c. Z- Value

d. P- Value

e. Conclusion (reject H₀ or do not reject H₀ )

Answer 1

Solution :

This is the higher tailed test .

The null and alternative hypothesis is

H₀ : p = 0.70

H_a : p > 0.70

= x / n = 240 / 300 = 0.8

P₀ = 0.470

1 - P₀ = 0.30

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.8- 0.70 / [(0.70 * 0.30) / 300]

= 3.78

P(z > 3.78) = 1 - P(z < 3.78) = 0.0001

P-value = 0.0001

= 0.05

P-value <

Reject the null hypothesis(H0).