A random sample of 40 college students has a mean earnings of $3120 with a sample standard deviation of $677 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to test a claim: μ > $3000.

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Mathematics

Skylar Cantu

20 August, 21:13

A random sample of 40 college students has a mean earnings of $3120 with a sample standard deviation of $677 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to test a claim: μ > $3000.

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Gillespie · Answer 1

Normal distribution

Step-by-step explanation:

From the statement we have the following information:

Average sample, m = $ 3120

Sample size, n = 40

Population standard deviation, sd = $ 677

Because we know the standard deviation of the population and that in addition the sample size is also greater than 30 (is 40) we can say that the distribution of university earnings is a normal distribution, that is, we can use the z test to build a confidence interval