Question 17 5 points Save Answer A tire manufacturer claims that his tires last

ID: 1140880 • Letter: Q

Question

Question 17 5 points Save Answer A tire manufacturer claims that his tires last at least 1,000 miles more than his competitor's. Two independent samples of 10 tires each are subjected to wear and the average life of the company's tires is found to be 16,700 miles, with a standard deviation of 1,700 miles. The competitor's tires last a mean of 15,100 miles, with a standard deviation of 1,350 miles. State the null hypothesis to test whether the manufacturer's claim is true. Assume that the manufacturer's tires are population 1 and the s tires are population 2. Ho: -u22 1,500 Ho: 1-u2 2,000 Ho: 1-2-2,000 O HO: -ups 1,000

Explanation / Answer

Given:

Tire manufacturers claim –

His company’s tires last 1000 miles more than that of the competitor’s.

The average age of company’s tires (P1) = 16,700 miles, SD = 1,700 miles

The average age of competitors tires (P2) = 15,100 miles, SD = 1,350 miles

To find:

State the null hypothesis to test whether the manufacturer’s claim is true.

Assumption:

Assume that the manufacturer’s tires are population 1 and the competitors are population 2.

Answer:

Ho = Tire manufacturer’s claim is correct, i.e.,

Ho = 1 > 2

Here, as per the sampling, the average age of the company’s tires are 16,700 miles with an SD of 1,700 miles.

Whereas, the average age of the competitor’s tires is 15100 miles with SD 1350 miles.

As we must test via Null hypothesis, then 1 > 2.

However, if the two standard deviations are larger than the difference between the two means, the hypothesis is not supported.

This is because, if SD is higher that the mean becomes highly unreliable claiming that the date is. widely spread

To test this statement,

Tire Types

Mean

Man’s

16,700

1,700

Competitor’s

15,100

1,350

As per the given data, (16,700 – 15,100) < (1,700,1,350 )

Therefore, it’s safe to assume that Ho = 1 - 2 =< 2000