Question

take the bus to work is 0.15. Is this significantly different from the statewide average of 0.10? Use a significance level of 0.05. Write down the null and alternative hypotheses, find the test statistic and the p-value, and state your conclusion. (8pts)

Answer 1

H0: p = 0.10

Ha: p $\neq$ 0.10

Test statistics

z = $\hat{p}$ - p / sqrt( p (1 -p) / n)

= 0.15 - 0.10 / sqrt( 0.10 * 0.90 / 50)

= 1.18

This is test statistics value.

p-value = 2 * P( Z > z)

= 2 * P( Z > 1.18)  

= 2 * 0.119

= 0.238

Since p-value > 0.10 level, Do not reject H0.

We conclude at 0.10 level that we fail to support the claim.