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A random sample of 10 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.

User Lamecca
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4 votes

Answer:

t-distribution should be used to test a claim : μ > $3000.

Explanation:

We are given that a random sample of 10 college students has a mean earnings of $3,120 with a sample standard deviation of $677 over the summer months.

We have to test a claim of μ > $3,000.

Since in this question we are provided with;

Sample mean earnings,
\bar X = $3,120

Sample standard deviation, s = $677

Sample of college students, n = 10

So, Null Hypothesis,
H_0 :
\mu \leq $3,000

Alternate Hypothesis,
H_a :
\mu > $3,000

The distribution that we will use here for our test statistics will be t-distribution because in the question we don't know anything about population standard deviation
(\sigma) .

Normal distribution is used when we know population standard deviation
(\sigma) .

So, the test statistics used will be One-sample t-test statistics;

Test statistics =
(\bar X -\mu)/((s)/(√(n) ) ) ~
t_n_-_1

Therefore, t-distribution should be used to test a claim: μ > $3000.

User Aberger
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