Answer:
<em>Null Hypothesis</em>: H₀ : μ < 214 miles
<em>Alternative Hypothesis :H₁</em>: 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:
<u><em>Step(i):-</em></u>
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
<u><em>Step(ii):-</em></u>
Null Hypothesis: H₀ : μ < 214 miles
Alternative Hypothesis :H₁: μ> 214 miles
Test statistic
![t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bx%5E%7B-%7D%20-mean%7D%7B%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
![t = \frac{198 -214}{\frac{42}{\sqrt{12} } }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B198%20-214%7D%7B%5Cfrac%7B42%7D%7B%5Csqrt%7B12%7D%20%7D%20%7D)
|t| = |- 1.319| = 1.319
Degrees of freedom = n-1 = 12 -1 =11
critical value ![t_{(0.005 , 11)} = 3.4966](https://tex.z-dn.net/?f=t_%7B%280.005%20%2C%2011%29%7D%20%3D%20%20%203.4966)
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