Question

A random sample of 23 items from the first population showed a mean of 112 and a standard deviation of 10. A sample of 17 items for the second population showed a mean of 106 and a standard deviation of 10. Use the 0.025 significant level. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.) State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal places.) What is your decision regarding the null hypothesis? Use the 0.03 significance level.

Answer 1

To find the degrees of freedom for an unequal variance test, calculate it using the given formula. The test statistic can be calculated and compared to the critical value to make a decision regarding the null hypothesis.

Step-by-step explanation:

To find the degrees of freedom for an unequal variance test, you need to calculate it using the formula: df = (s1^2/n1 + s2^2/n2)^2 / [(s1^2/n1)^2 / (n1 - 1) + (s2^2/n2)^2 / (n2 - 1)]. In this case, the sample size for the first population is 23 and the sample size for the second population is 17. Substitute the given values into the formula to find the degrees of freedom. The decision rule for a 0.025 significance level is to reject the null hypothesis if the test statistic is greater than the critical value. The test statistic can be calculated using the formula: t = (mean1 - mean2) / sqrt( (s1^2/n1) + (s2^2/n2) ). Substitute the given values into the formula to calculate the test statistic. The decision regarding the null hypothesis depends on comparing the test statistic with the critical value.