The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set α = 0.05. The conclusion for this hypothesis test would be that because the test statistic is ______________________________________.

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dfbustos dfbustos · Answer 1 · 2020-07-15T02:57:43+02:00

Answer:

[tex]z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29[/tex]

Step-by-step explanation:

information given

[tex]\bar X=10.6[/tex] represent the sample mean

[tex]\sigma=4.1[/tex] represent the population standard deviation

[tex]n=45[/tex] sample size

[tex]\mu_o =12[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.

z would represent the statistic

[tex]p_v[/tex] represent the p value for the test

Hypothesis to test

We want to test if the true mean is less than 12, the system of hypothesis would be:

Null hypothesis:[tex]\mu \geq 10[/tex]

Alternative hypothesis:[tex]\mu < 10[/tex]

The statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)

Replacing the info given we got:

We can replace in formula (1) the info given like this:

[tex]z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29[/tex]