Question

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is:_________

a. H_0: μ < 40,000 H_a: μ >= 40,000
b. H_0: μ <= 40,000 H_a: μ > 40,000
c. H_0: μ > 40,000 H_a: μ <= 40,000
d. H_0: μ >= 40,000 H_a: μ < 40,000

Answer 1

Answer:

Option B)

$H_{0}: \mu \leq 40,000\text{ miles}\\H_a: \mu > 40,000\text{ miles}$

Step-by-step explanation:

We are given the following in the question:

Population mean = 40,000 mile

A hypothesis is conducted that the new production process increases the life expectancy of tires.

Thus, the null and the alternate hypothesis

$H_{0}: \mu \leq 40,000\text{ miles}\\H_a: \mu > 40,000\text{ miles}$

The null hypothesis states that the life expectancy of the tires remain the same after the new production process as the population of the tire and the alternate hypothesis states that the life expectancy of the tire increases and the mean life is greater than 40,000 miles.

Thus, the correct answer is

Option B)

$H_{0}: \mu \leq 40,000\text{ miles}\\H_a: \mu > 40,000\text{ miles}$

Answer 2

Answer:

$H_0$ : μ <= 40,000 $H_a$ : μ > 40,000

Step-by-step explanation:

We are given that the average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased.

We have to test the validity of the management belief.

For this firstly as we know that the testing is always done the population parameter;

Let $\mu$ =  average life expectancy of tires produced by new production process

So, Null Hypothesis, $H_0$ : $\mu \leq$ 40,000  

Alternate Hypothesis, $H_a$ : $\mu$ > 40,000  

Here, null hypothesis states that the average life expectancy of tires produced through a new production process is less than or equal to 40,000 miles.

Similarly, alternate hypothesis states that the average life expectancy of tires produced through a new production process is greater than 40,000 miles or it is increased.

So, this is the correct set of hypothesis that would be used for conducting the test.