Question

Question 1) Llantas Inc. claims that the average life of a certain tire is greater or equal than 25,000 miles under normal driving conditions (assume that the population is normally distributed). A random sample of 16 tires is tested. The mean of the sample is 24,000 miles and the standard deviation of the sample is 4,000 miles. What is the critical value? Use alpha = .05.

Question 1 options:

1) -1.00

2) -1.753

3) -1.645

4) 1.753

Question 2 (5 points)

Llantas Inc. claims that the average life of a certain tire is greater or equal than 25,000 miles under normal driving conditions (assume that the population is normally distributed). A random sample of 16 tires is tested. The mean of the sample is 24,000 miles and the standard deviation of the population is 4,000 miles. What is the critical value? Use alpha = .05.

Question 2 options:

	1) -1.00
	2) -1.96
	3) -1.645
	4) 1.96

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 25000

H_a : $\mu$ > 25000

1) $\alpha$ = 0.05

degrees of freedom = n - 1 = 16 - 1 = 15

P(t > t) = 0.05

= 1 - P(t < t) = 0.05

= P(Z < z) = 1 - 0.05

= P(t < 1.753 ) = 0.95  

critical value t* = 1.753

2) $\alpha$ = 0.05

standard deviation is known,

P(Z > z) = 0.05

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < 1.645 ) = 0.95  

critical value z* = 1.645