Question

In recent commercials Toyota claimed that 80% of its vehicles sold in the past 20 years are still on the road. You work for an agency that wants to test this claim. You are willing to accept Toyota's claim unless there is statistically significant evidence that it is false. You have a limited budget, but you want to get the most accurate results you can. Describe, from beginning to end, how you would run your study. Use as many concepts you learned in this course as possible to get maximum credit. HTML EditorKeyboard Shortcuts

Answer 1

Explanation:

We have to perform one sample proportion test. To do so we have to proceed through following steps.

(1) We have to collect data about vehicle sales in last 20 years.

(2) Using random number table or random number generator or otherwise we have to select sample of vehicles from the list of sale. In this step, we have to keep an eye on the fact that sample is to be selected from all years (all of 20). Using stratified random sampling by dividing vehicles sold over different years is an effective way to do so. That means, we may divide vehicles sold into 20 homogeneous strata over 20 years and select sample from each strata.

(3) After selecting sample of vehicles we have to communicate to corresponding vehicle owners to gather information about that particular vehicle.

(4) We have to note number of vehicles which are still on the road.

Suppose, we have selected n vehicles as sample and after communicating we found that \tiny r of those are still on the road.

We have to test for null hypothesis
`H_0:p=0.80`

against the alternative hypothesis
`H_1 \\eq 0.80`

Our test statistic is given

`z=(\hat p - p_0)/(√(p_0(1-p_0)/n) )`

here,

`\hat p =(r)/(n)`

`p_0 =0.80`

`z=(r/n-0.80√(n) )/(0.40) \\\\=2.5((r)/(n) -0.8)√(n)`

We then calculate corresponding p-value.

We reject our null hypothesis if
`\text{p-value}<\alpha` , level of significance.

According to our obtained p-value and level of significance we proceed to certain conclusion.