Purchase Solution

Central Limit Theorem and single sample hypothesis test

Not what you're looking for?

Ask Custom Question

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.

Purchase this Solution

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.

Solution Preview

This problem deals with the distribution of the sample mean. I have attached a Word document explaining how the sample mean is distributed according to the Central Limit Theorem. Once the distribution of the sample mean is determined, the probability of interest can be calculated using normal probability tables. ...

Purchase this Solution

Free BrainMass Quizzes
Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.