Question

Check my work It is advertised that the average braking distance for a small car traveling at 70 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 35 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test. O Ho: - 120; HA: 4120 Ho: u 120; HA u < 120 Ho: u$ 120; HA" > 120 b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic Rrou

Answer 1

(a)

Null hypothesis H0 : $\mu$ = 120

Alternate Hypothesis H1: $\mu \neq$ 120

(b)

We will be using the one sample t - test for this problem:

t in

where $\overline{x}$ = sample mean = 111

$\mu$ = hypothesized value of mean = 120

$\sigma$ = population standard deviation = 21

n= sameple size = 35

$t = \frac{111-120 }{\frac{21 }{\sqrt{35}}}$

$t = \frac{-9 }{\frac{21 }{5.9160}} = \frac{-9}{3.5497} = -2.5354$

(b) The p value is 0.016014

Therefore, 0.01 < p value < 0.025 and the result is significant, so , we reject the null hypothesis.

(c) At 0.1 level of significane, the result is significant because 0.016014 < 0.1

Therefore, we reject the null hypothesis.

The average breaking distance is different from 120 feet.