Question

7. In questions 7, and 8, suppose 1% of all cars are stolen every year. An anti-theft system manufacturer claims that only 0.3% of all cars equipped with their system are stolen. A consumer advocacy group intending to evaluate this claim, tracks 12000 cars equipped with the anti-theft system and found that 30 of them were stolen in the first six months of 2017. Assuming that the first 6 months of the year are no different from the second 6 months of the year in terms of number of theft, what are the H0 and H1 in the study run by the consumer advocacy group? (Hint: P is defined as the proportion of cars stolen every year) A. H0: P=0.003 , H1: P is not equal to 0.003 B. H0: P=0.003 , H1: P is less than 0.003 C. H0: P=0.003 , H1: P is more than 0.003 D. H0: P=0.003 , H1: P = 0.0025 E. H0: P=0.003 , H1: P = 0.005

8.What is the value of the test statistics, and what do you conclude at 95% confidence level?. (Hint: Our sample is only from tracking cars for 6 months, not the entire year, so what does our 6 months sample indicate about the proportion of stolen cars in 12 months? That is how you find P^) A. z=3, so we reject the H0, and the anti-theft system manufacturer’s claim is valid B. z=4, so we reject the H0, and the anti-theft system manufacturer’s claim is valid C. z=3, so we reject the H0, and the anti-theft system manufacturer’s claim is invalid D. z=4, so we reject the H0, and the anti-theft system manufacturer’s claim is invalid

Answer 1

Question 7

A. H₀: p = 0.003, H₁: p ≠ 0.003

Explanation:

The claim is given as only 0.3% of all cars equipped with anti-theft system are stolen. This is the null hypothesis. There is no mention whether the proportion decrease or increase so we use two tailed test. We only want to check whether the population proportion is 0.3% or not.

Question 8

We are given x = 30 for six months. So, x would be 30*2 = 60 for one year.

We have n = 12000

Confidence level = 95%, so

Level of significance = α = 0.05

Sample proportion = P = x/n = 60/12000 = 0.005

Test statistic formula is given as below:

Z = (P – p)/sqrt(pq/n)

Where, P is sample proportion, p is population proportion, q = 1 – p, and n is sample size.

We are given n = 12000, p = 0.003, q = 1 – 0.003 = 0.997, P = 0.005

Z = (0.005 – 0.003)/sqrt(0.003*0.997/12000)

Z = 4.0060

P-value = 0.0001

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is insufficient evidence to conclude that only 0.3% of all cars equipped with anti-theft system are stolen.

D. z=4, so we reject the H0, and the anti-theft system manufacturer’s claim is invalid