Question

In 1999, 2.2% of all cars in the United States were reported stolen. In a random sample of 400 Nissan Maxima cars that year, 12 were reported stolen. Is this evidence (at the  = 0.05 level) that the theft rate for this model is higher than the national rate?

Answer 1

The evidence is not sufficient to suggest that the theft rate of Nissan Maxima cars are higher than national rate

Explanation:

The number of cars that where reported stolen in 1999 = 2.2% = 0.022

The number of Nissan Maxima cars in the sample = 400

The number of Nissan Maxima cars that were reported stolen = 12

The level of significance, α = 0.05 level

The critical-z at 0.05 = 5% level = 1.645

The percentage of Nissan Maxima cars reported stolen,
`\hat p` = 12/400×100 = 3%

The test statistic is given as follows;

`z=\frac{\hat{p}-p_0}{\sqrt{(p_0 \cdot (1 - p_0))/(n)}}`

Therefore

`z=\frac{0.03-0.022}{\sqrt{(#0.022 \cdot (1 - #0.022))/(400)}} \approx 1.0908`

The test statistic = 1.0908

The p-value P(Z > 1.0908) = 1 - P(Z > 1.0908) = 1 - 0.86214 = 0.13768

Given that the critical-z is larger than the absolute value of the test statistic, the given data is statistically insignificant, we fail to reject the null hypothesis

There is not enough statistical evidence to suggest that the theft rate of Nissan Maxima cars are higher than national rate.