Question

Help Save & Edt Subr 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 folse, meaning it is different than advertised. 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. State the null and alternative hypotheses. Using the critical value approach, test the hypotheses at the 5% level of significance. Which of the following is the best conclusion to draw for this test? Multiple Choice Since the calculated tests Z-154 is equal to the chocol value-164, at the 0.05 level of significance we do not reject the null hypotheses Since the critical value-154 is greater than the calculated at 2--220. the 0.05 level of significance we reject the null hypothesis and conclude that the braking distance is less than 120 Since the calculated test sta Z-164 between the chce 196, at the 0.05 level of significance we do not reject the null hypothesis Since the calculated test Z-6415 greater than the calve 195, the 0.05 level of significance we seen hypothes

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The average braking distance for cars is 120 feet.

Alternative hypothesis: H_a: The average braking distance for cars is different than 120 feet.

H₀: µ = 120 versus H_a: µ ≠ 120

This is a two tailed test.

The test statistic formula is given as below:

Z = (x̄ - µ)/[σ/sqrt(n)]

From given data, we have

µ = 120

x̄ = 114

σ = 22

n = 36

α = 0.05

Critical value = ±1.96

(by using z-table or excel)

Z = (114 - 120)/[22/sqrt(36)]

Z = -1.64

P-value = 0.1018

(by using Z-table)

P-value < α = 0.05

Test statistic value -1.64 is lies between critical values -1.96 and 1.96.

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the average braking distance for cars is different than 120 feet.

Answer:

Since the calculated test statistic z = -1.64 is between the critical values +/- 1.96, at the α = 0.05 level of significance we do not reject the null hypothesis.