Question

describe how to stimulate the distribution of the test statistic, assuming joe has the same ability with both weights

Answer 1

To simulate the distribution of the test statistic, define the null hypothesis, select the appropriate test statistic, apply the Central Limit Theorem for calculating the mean and standard deviation of the uniform distribution, calculate the test statistic, and compare it to the critical value.

Step-by-step explanation:

To simulate the distribution of the test statistic assuming Joe has the same ability with both weights, you can perform the following steps:

1. Firstly, define the null hypothesis which states that Joe's ability with both weights is identical.
2. Then, identify the appropriate test statistic for comparing two means, which is likely a t-test or an F-test for variance if you're comparing variability.
3. Given that the underlying distribution of weights is uniform, you need to use the Central Limit Theorem to assume that the sum or average of the samples will be approximately normally distributed if the sample size is sufficiently large.
4. With a uniform distribution of weights between 24 and 26 pounds, you would calculate the mean and the standard deviation of the distribution. For a uniform distribution, the mean is (a+b)/2 and the variance is (b-a)^2/12 for lower and upper limits a and b, respectively.
5. As the sample size is 100, which is large, the sample means will be normally distributed around the population mean with a standard deviation equal to the population standard deviation divided by the square root of the sample size (Central Limit Theorem).
6. Use this information to calculate the test statistic either manually or using a statistical software package.
7. Finally, compare the calculated test statistic to the appropriate critical value from the t-distribution or F-distribution table to determine whether to accept or reject the null hypothesis.

If you're looking at an F-test to compare variances, you'll need the ratio of the variances, not the means. Ensure you have the correct test for your hypothesis.

Remember, the Central Limit Theorem applies regardless of the shape of the population distribution, as long as the sample size is sufficiently large. In problems like this, it is critical for approximating the sampling distribution of the test statistic.