Question

In 2019, 71% of all motor vehicle accidents were driven by males. In your town, a random sample of 180 motor vehicle accidents was taken, and it was found that 132 of them had male drivers. You conduct a hypothesis test of:

H0: p = 0.71 (null hypothesis, where p is the population proportion of accidents driven by males)
HA: p > 0.71 (alternative hypothesis)

What is the correct z statistic for this test?

(a) 0.245
(b) 0.690
(c) 1.961
(d) 2.345

Answer 1

The correct z statistic for the hypothesis test on the population proportion of accidents driven by males is 0.690.

Step-by-step explanation:

To calculate the correct z statistic for this hypothesis test, we will use the formula z = (p' - p0) / sqrt[p0(1 - p0) / n], where p' is the sample proportion, p0 is the hypothesized population proportion, and n is the sample size.

First, let's find the sample proportion p':
p' = 132 / 180 = 0.7333 (rounded to four decimal places).

Then we plug in the values into the z formula:
z = (0.7333 - 0.71) / sqrt[0.71(1 - 0.71) / 180]
z = 0.0233 / sqrt[0.2059 / 180]
z = 0.0233 / sqrt[0.001144]
z = 0.0233 / 0.033819 (rounded to six decimal places)
z = 0.6888 (rounded to four decimal places).

So the correct z statistic for this test is 0.690, which corresponds to option (b).