Question

According to Time magazine (June 11, 2012), 33% of all cars sold in the United States are SUVs. Suppose a random sample of 500 recently sold cars shows that 141 are SUVs.

a) Write the null and alternative hypotheses to test that the proportions of SUVs sold in the US is different from 33%

b) Based on the sample above the one proportion Z test produced a P-value = 0.022. State your decision regarding H0 and Ha at 5% level of significance.

c) Based on the same sample the 95% confidence interval is (0.2429, 0.3237). Does the confidence interval support your decision in part b. Explain.

Answer 1

Part a

Null hypothesis: H0: the proportion of SUVs sold in the US is 33%.

Alternative hypothesis: Ha: the proportion of SUVs sold in the US is different from 33%.

H0: p = 0.33 versus Ha: p ≠ 0.33

This is a two tailed test.

Part b

We are given

P-value = 0.022 < α = 0.05

So, we reject the null hypothesis H0

There is sufficient evidence to conclude that the proportion of SUVs sold in the US is different from 33%.

Part c

The confidence interval supports the decision in part b, because the value 0.33 is not containing in the given confidence interval.