Question

Harley-Davidson motorcycles make up 14% of all motorcycles registered in the United States. In 1995, 9224 motorcycles were reported stolen; 2490 of these were Harleys. We can think of motorcycles stolen in 1995 as an SRS of motorcycles stolen in recent years.

Is the proportion of Harleys among stolen bikes significantly higher than their share of all motorcycles? (10 pts)
A. Set the null and alternative hypothesis (2 pt)

B. Find the z statistic and p value (4pt)

C. Make your statement based on significance level 0.05 (4pt)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.14

H_a : p > 0.14  

= x / n = 2490 / 9224 = 0.2699

P₀ = 0.14

1 - P₀ = 0.86

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2699 - 0.14 / [(0.14 * 0.86) / 9224]

= 35.97

P(z > 35.97) = 1 - P(z < 35.97) = 0

P-value = 0

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that the proportion of Harleys among stolen bikes significantly

higher than their share of all motorcycles .