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Help Save & Edt Subr It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals
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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: Ha: The average braking distance for cars is different than 120 feet.

H0: µ = 120 versus Ha: 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.

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