A scrap metal dealer claims that the mean of his sales is "no more than $80," but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchase to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed and using the 0.05 level of significance, is the agent’s suspicion confirmed?

There is enough not evident to support dealer's claim that his sales is no more than $80.                              

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $80

Sample mean, = $91

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = $21

First, we design the null and the alternate hypothesis

We use one-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                        

The calculated test statistic is greater than the critical value, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

There is enough not evident to support dealer's claim that his sales is no more than $80.

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step-by-step explanation:

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