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Central Limit Theorem and single sample hypothesis test

A spokesman for a popular television game show claims that contestants on the show win an average of $1200. In a random sample, 35 contestants were questioned on the amount of money they had won in order to test the hypothesis.

The null hypothesis or Ho: the population mean equals $1200,
The alternative Hypothesis or Ha: the population mean is not equal to $1200.

A. Suppose the mean win for the sample of 35 contestants turns out to be $1045. Assuming the null hypothesis is true, what is the probability of obtaining a sample mean value of $1045 or more? (Use 325 as the population standard deviation.)

B. Does a sample mean of $1045 provide evidence that the null hypothesis is false? Explain your answer.

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This problem deals with the distribution of the sample mean. I have attached a Word document explaining how the ...

Solution Summary

In this problem, we use the central limit theorem to find the distribution of a sample mean. Then we use that distribution to find the probability that the sample mean from a random sample exceeds a particular value. The probability we find is converted into the p-value then used to test the hypothesis of interest.