Question

In a state with 20,000 voters, a sample of 500 is taken to estimate what proportion each of 4 candidates support is for governor. The results are 192 support candidate w, 160 support candidate x, 97 support candidate y, and 51 support candidate z.
1. Estimate p, the proportion that support candidate w in the population, calculate a bound on the error of estimation.
2. Is there a difference in proportion of voters supporting candidates w and x? Explain why.

Answer 1

1:

The sample proprotion is:

The critical value of z for 95% confidence interval is 1.96.

The bound on the error of estimation is

2;

Here the claim (alternative hypothesis) is

So test is two tailed. Following is the null hypothesis:

Here we have

Pooled sample proportion is

Standard error of the test is:

So test statistics will be

The p-value is: 0.0170

Excel function used for p-value: "=2*(1-NORMSDIST(2.12))"

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that there is a significant difference in proportion of voters supporting candidates w and x.