Question

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ = 82.5 H a : μ > 82.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 103.6 114.4 108 108.9 What is the test statistic for this sample?

Answer 1

To test the claim at a significance level of 0.01 with an unknown standard deviation, we can use the t-test. The test statistic for this sample is 4.219.

Step-by-step explanation:

To test the claim at a significance level of 0.01 with unknown standard deviation, we can use the t-test. The null hypothesis, H_0, states that the mean, μ, is equal to 82.5. The alternative hypothesis, H_a, states that the mean is greater than 82.5.

Using the given data: 103.6, 114.4, 108, and 108.9, we can calculate the sample mean and the sample standard deviation. With these values, we can then find the test statistic using the formula:

t-test statistic = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Substituting the values, we get:

t-test statistic = (111.225 - 82.5) / (5.6845 / sqrt(4)) = 4.219