Question

Suppose I’m trying to determine whether to reject or fail to reject the null hypothesis that the country has less than or equal to 70% of people that believe the country is going in the wrong direction. If this is not true then I hypothesize that it could be larger than 70%. I’ve also taken a survey of size 50 and have found the sample percentage to be 75%. My alpha value is .05.

1. Write the null and alternative hypotheses:

2. Write down and compute test statistic:

3. Draw Rejection Region

4. Suppose the p-value is .06

5. State your conclusion about the null hypothesis:

Answer 1

N = 50, = 0.75

1) Null and Alternative Hypotheses :

2) Test Statistics :

3) Rejection Region :

At =0.05, right tailed critical value from standard normal table, z_c = 1.64

Rejection region for this right-tailed test is R = {z:z>1.64}

4) Decision about the null hypothesis :

Since it is observed that z = 0.7715 < z_c = 1.64, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = NORM.S.DIST(0.7715, 0) = 0.2963, and since p = 0.2963 > 0.05, it is concluded that the null hypothesis is not rejected.

5) Conclusion:

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion is greater than 0.70 ​, at 0.05 significance level.

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