80.0k views
0 votes
An insurance company claims the average car on the road is less than 6 years old. Based on a random sample of 15 cars, the mean age is 5.8 years with a standard deviation of 1.1 years. Does the sample support the insurance company's claim?

1 Answer

4 votes

Answer: No, we do not have enough evidence to support the insurance company's claim.

Explanation:

Let
\mu be the average car on the road .

As per given , we have

Null hypothesis :
H_0:\mu\geq6

Alternative hypothesis :
H_a:\mu<6

Since ,
H_a is left-talied and population standard deviation is unknown , so we perform a left-tailed t-test.

Test statistic :
t=\frac{\overline{x}-\mu}{(s)/(√(n))} , where
\overline{x}= sample mean , s= sample standard deviation , n= sample size .

Put
\overline{x}= 5.8 years , s= 1.1 years , n= 15 .


t=(5.8-6)/((1.1)/(√(15)))\approx-0.704

Also, At 0.05 significance ,


t_(critical)=1.75305 (by t-distribution table)

Decision : Since
|t_(calculated)|<|t_(critical)| \ [\ \because\ 0.704<1.75305] , so we fail to reject the null hypothesis .

Conclusion : At 5% confidence level , we do not have enough evidence to support the insurance company's claim.

User CubeJockey
by
7.3k points