The speed limit on a road is 45 mph. you want to clock the speed of a random sample of cars to test the hypothesis that the average speed of cars is greater than the speed limit. what kind of test would you use?

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22-03-2022
Mathematics

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The speed limit on a road is 45 mph. you want to clock the speed of a random sample of cars to test the hypothesis that the average speed of cars is greater than the speed limit. what kind of test would you use?

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astha8579 astha8579 · Answer 1 · 2022-03-30T13:35:30+02:00

The test that we would use to test the hypothesis that the average speed of cars is greater than the speed limit is: One sample t-test

When do we use one sample t-test?

When we want to find out from the sample if the unknown population mean is different from some specific value, then we can use one sample t-test.

The test statistic is:

[tex]t = \dfrac{\overline{x} - \mu_0}{s/\sqrt{n}}[/tex]

where we have:

[tex]\overline{x}[/tex]= mean of the sample
s = sample standard deviation
[tex]\mu_0[/tex] = the specific value we're comparing population mean with.
n = sample size
degree of freedom = n - 1

For this case, we want to test the hypothesis that the average speed of cars is greater than the speed limit.

That means we want to know if

unknown population mean (the average speed of cars) > speed limit (45).

symbolically, we want to test if [tex]\mu > 45[/tex] (in miles per hour)

Thus, the test that we would use to test the hypothesis that the average speed of cars is greater than the speed limit is: One sample t-test

Learn more about one sample t-test here:

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