Question

State the hypothesis and claim:

Answer 1

Answer:

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

Step-by-step 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

             $t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }$

             $t = \frac{198 -214}{\frac{42}{\sqrt{12} } }$

          |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