Question

Government officials claim that no more than 29% of the residents of a state are opposed to building a nuclear plant to generate electricity. Local conservation groups claim that the true percentage is much higher. To test the government’s claim, an independent testing group selects a random sample of 81 state residents and finds that 29 of the people are opposed to the nuclear plant.

(a) What is the variable? Is it an attribute or measurable?

(b) State the hypotheses

(c) Calculate the value of the test statistic and the p-value?

(d) Would you reject H0 or fail to reject H0 at 5% level of significance?

(e) What would you conclude about the government’s claim?

Answer 1

Solution :

This is the lesst tailed test .

The null and alternative hypothesis is

H₀ : p =0.29

H_a : p <0.29

= x / n = 29/81=0.3580

P₀ = 0.29

1 - P₀ = 1-0.29=0.71

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3580-0.29/ [(0.29*0.71) / 81]

Z=1.35

P(z <1.35 ) = 0.9115

P-value = 0.9115

= 0.05

P-value >

do not Reject the null hypothesis .

There is no sufficient evidence to suggest that