Question

Q.5. From a sample of 100 tires the mean life time was 46000 miles with a standard deviation of 5500 miles. Test the hypothesis μ = 45000 against the alternate μ > 45000 at (i) 0.05 and (ii) 0.01 level of significance. ?

solve the above problem step by step in proper format

Answer 1

Solution :

Given that ,

= 45000

= 46000

= 5500

n = 100

This will be a two tailed test because the alternative hypothesis is showing a specific direction

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 45000

H_a : > 45000

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 46000 - 45000) / 5500 / 100

= 1.82

The test statistic = 1.82

P - value = P(Z > 1.82) = 1 - P (Z < 1.82 )

= 1 - 0.9656

= 0.0344

P-value = 0.0344

(i) = 0.05  

0.0344 < 0.05

P-value <

Reject the null hypothesis .

(ii)   = 0.01

0.0344 > 0.01

P-value >

Fail to reject the null hypothesis .