Question

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 36 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 114 feet. Assume that the population standard deviation is 22 feet.

Answer 1

Answer:

We conclude that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet which means that the statement made in the advertisement is correct.

Step-by-step explanation:

We are given that it is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false.

She randomly test drives 36 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 114 feet. Assume that the population standard deviation is 22 feet.

Let $\mu$ = average braking distance for a small car traveling at 65 miles per hour.

So, Null Hypothesis, $H_0$ : $\mu$ = 120 feet     {means that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 120 feet     {means that the average braking distance for a small car traveling at 65 miles per hour is different from 120 feet}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                        T.S. =  $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\bar X$ = sample average braking distance = 114 feet

            $\sigma$ = population standard deviation = 22 feet

            n = sample of small cars = 36

So, test statistics  =  $\frac{114-120}{\frac{22}{\sqrt{36} } }$  

                               =  -1.64

The value of z test statistics is -1.64.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet which means that the statement made in the advertisement is correct.