Question

Do you typically stop or speed up at a yellow traffic light?

Ho: proportion who speed up = 0.70 Ha: proportion who speed up ≠ 0.70

The sample size is 32 and the focus is on who does speed up at the light.

How many speeding tickets have you had in your life?

Ho: average tickets = 5 Ha: average tickets ≠ 5

Average: 7.03 Standard Deviation: 10.00

Test the hypotheses and include a full calculation of the test statistic, p-value, and stat the full conclusion in words for both problems. Show all work.

Answer 1

1. Let p be the proportion who speed up at a yellow traffic light. We have to test, H0: p = 0.7 against H1: p 0.7

The test-statistic is given by, Z = .

2. We have to test, H0: = 5 against H1: 5

The test-statistic is given by, Z = = = 1.1483

Under H0, Z ~ N(0,1)

The p-value = 2 P(Z > 1.1483) = 2 * 0.1254 = 0.2508

Since, p-value > level of significance (assuming 5% level of significance), we fail to reject H0.

We conclude that the average number of tickets is not significantly different from 5.