Question

State the hypothesis and claim:

The expense of moving the storage yard for the consolidated Package Delivery Service is justified only if it can be shown that the daily average travel distance is less than 214 mi. In 12 trial runs the average distance was 198 mi with a standard deviation of 42 mi At a = .01 test the claim that the average daily travel distance is less than 214 mi.


the claim is _____. H0: ___ H1: ____

Answer 1

Null Hypothesis: H₀ : μ < 214 miles

Alternative Hypothesis :H₁: μ> 214 miles

The calculated value |t| = 1.319 < 3.4966 at 0.01 level of significance

Null hypothesis is accepted

The average daily travel distance is less than 214 miles

Explanation:

Step(i):-

Given that the size of the sample 'n' = 12

The mean of the Population = 214 miles

The mean of the sample = 198 miles

The standard deviation of the sample = 42 miles

Level of significance = 0.01

Step(ii):-

Null Hypothesis: H₀ : μ < 214 miles

Alternative Hypothesis :H₁: μ> 214 miles

Test statistic

`t = (x^(-) -mean)/((S.D)/(√(n) ) )`

`t = (198 -214)/((42)/(√(12) ) )`

|t| = |- 1.319| = 1.319

Degrees of freedom = n-1 = 12 -1 =11

critical value
`t_((0.005 , 11)) = 3.4966`

The calculated value |t| = 1.319 < 3.4966 at 0.01 level of significance

Null hypothesis is accepted

The average daily travel distance is less than 214 miles