Question

Question No 4

1. Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α. (Marks 1.5)

Left -tailed test

z = -1.52

α = 0.04

2. A trucking firm suspects that the mean life of a certain tire it uses is less than 35,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,450 miles with a standard deviation of 1200 miles. At α = 0.05, test the trucking firmʹs claim. (Marks 2)

Answer 1

Solution :-

Given :-

z = - 1.52 ( Left tailed test ) , = 0.04

By using Standard Normal ' z ' table

P ( z < -1.52 ) = 0.0643

P - Value = 0.0643

Since P- Value ( 0.0643 ) > ( 0.04 )

Decision : - Fail to reject Ho.

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Solution :-

Given :-

Mean (µ ) = 35000

Sample Mean ( x bar ) = 34450

Sample Standard deviation ( s ) = 1200

Sample Size ( n ) = 18

Significance level (α ) = 0.05

Df = n – 1 ; Df = 18 - 1 ; Df = 17

Hypothesis : -

Ho : µ = 35000

H1 : µ < 35000   ( This is Left tailed test )

Test statistic :-

t = ( x bar – µ ) / ( s / √ n )

t = ( 34450 - 35000 ) / ( 1200 / √ 18 )

t = - 1.94

t critical :- By using ‘ t ‘ distribution table at α = 0.05   and df = 17

t critical ( tc ) = - 1.740

P – value :- By using P value approach,P value at t = - 1.94 and df = 17

P – value = 0.0346

Decision :- Since P Value (0.0346 )   < α ( 0.05 )

                    Reject Ho.

Conclusion :- Therefore there is enough evidence to claim that population Mean is Less than 35000 at  α = 0.05.