Question

1.
A random sample of 45 individuals provide 32 Yes responses.

1. What is the point estimate of the proportion of the population that would provide Yes responses?
2. What is your estimate of the standard error of the sample proportion, σp?
3. Construct the 95% confidence interval for the population proportion.
4. Consider the alternative hypothesis Ha:p<0.8. Conduct the test with the rejection region approach with the 5% significance level.
5. Calculate the p-value for the test in part d and draw your conclusion.

Answer 1

1.a. Point estimate of proportion is

b. Standard error is

c. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

Hence CI is

d. Here hypothesis is

So test statistics is

The z-critical value for a left-tailed test, for a significance level of α=0.05 is

zc​=−1.64

Graphically

As test statistics do not fall in the rejection region, we fail to reject the null hypothesis

e. P value is

As P value is greater than alpha we fail to reject the null hypothesis

Hence we do no have sufficient evidence to support the claim that p<0.8