Question

You are trying to find the proportion of a Congressional district voters that support re-electing the incumbent Congressman. You sample 1000 people and find that only 49% of the sample favors re-electing him.

1. Find a 95% confidence interval estimate of the true population proportion that favors the incumbent Congressman.

2. Suppose that you believe that 51% of the Congressional district voters support re-electing the Congressman. Does this mean that you will reject our original hypothesis? Complete a hypothesis test at a 10 percent level of significance.

Answer 1

Answer:

Given,

n = 1000

pbar = 0.49

For 95% confidence interval ,Z value = 1.96

Now consider,

Interval = (pbar +/- Z*sqrt(pbar(1-pbar)/n))

= (0.49 +/- 1.96*sqrt(0.49(1-0.4)/1000))

= (0.49 +/- 0.030984)

= (0.49 - 0.030984 , 0.49 + 0.030984)

Interval = (0.459 , 0.521)

Test statistic:

Z = pbar - po/(sqrt(po(1-po)/n))

= (0.49 - 0.51)/(sqrt(0.51(1-0.51)/1000))

Z = -1.265

Now critical value = Z0.1/2 = Z0.5

Critical value = 1.645

Here Z value is less than the critical value so that we fail to reject the Ho and hence it is not significantly different from 51%