Question

9. When 200 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 3.47 years. Calculate the appropriate test statistic to test the claim that the mean for all car owners is less than 7.5 years.

Answer 1

The appropriate test statistic to test the claim that the mean for all car owners is less than 7.5 years is -1.997.

Explanation:

We are given that 200 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 3.47 years.

Let
`\mu` = mean for all car owners.

So, Null Hypothesis,
`H_0` :
`\mu \geq` 7.5 years {means that the mean for all car owners is more than or equal to 7.5 years}

Alternate Hypothesis,
`H_A` :
`\mu` < 7.5 years {means that the mean for all car owners is less than 7.5 years}

The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

T.S. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean length of time = 7.01 years

s = sample standard deviation = 3.47 years

n = sample of cars = 200

So, test statistics =
`(7.01-7.5)/((3.47)/(√(200) ) )` ~
`t_1_9_9`

= -1.997

Hence, the appropriate test statistic to test the claim is -1.997.