Question

1. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 71% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 68 %. Testing at the 0.02 level, is there enough evidence to support the strategist's claim? State the null and alternative hypotheses.

2. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 71% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 68 %. Testing at the 0.02 level, is there enough evidence to support the strategist's claim? Find the value of the test statistic.
3. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 71% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 68 %. Testing at the 0.02 level, is there enough evidence to support the strategist's claim? Specify if the test is one-tailed or two-tailed.
4. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 71 % of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 68 %. Testing at the 0.02 level, is there enough evidence to support the strategist's claim? Determine the P-value of the test statistic.
5. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 71% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 68 %. Testing at the 0.02 level, is there enough evidence to support the strategist's claim? Identify the value of the level of significance.
6. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 59% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 54%. Make the decision to reject or fail to reject the null hypothesis at the 0.01 level.
7. The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 71% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 68 %. Testing at the 0.02 level, is there enough evidence to support the strategist's claim? State the conclusion of the hypothesis test.

Answer 1

See step by step explanation

Explanation:

Sample size n = 800

p₁ = 71 % p₁ = 0,71 and q₁ = 0,29

Claim from political strategy wants evaluation to see if that sample implies that residents who favor the construction are more than 68 %

Then

p₀ = 68% p₀ = 0,68

Sample size 800 big enough to use the approximation of binomial distribution to normal distribution

1) Hypothesis Test

Null Hypothesis H₀ p₁ = p₀

Alternative Hypothesis Hₐ p₁ > p₀

2)Test Statistics z (s)

z(s) = ( p₁ - p₀ ) / √p₁*q₁/n

z(s) = 0,03 / √0,71*0,29/800

z(s) = 0,03 / 0,016

z(s) = 1,875

3) In the problem statement the expression " more than " has to be formulated in the alternative hypothesis and indicates that the test is one tail test to the right

4) z(s) = 1.875 from z-Table we get p-value = 0,030

Now significance level is α = 0,02

Therefore p-value > 0.02

Then that value corresponds to the acceptance region for H₀.

We don´t have enough evidence to support the strategist´s claim

5) The level of significance is α = 0,02

6) If now we change α to be equal to 0,01 α = 0,01

p-value > 0,01 and still we have to accept H₀

7) We accept H₀ we are not able to support strategist´s claim