Question

The null and alternate hypotheses are: H0:μ1≤μ2 H1:μ1>μ2 A random sample of 27 items from the first population showed a mean of 114 and a standard deviation of 15: A sample of 15 items for the second population showed a mean of 106 and a standard deviation of 9 . Assume the sample populations do not have equal standard deviations and use the 0.025 significant level. Required: a. Find the degrees of freedom for unequal variance test. (Round down your onswer to the nearest whole number.) b. Stote the decision rule for 0025 significance level (Round your answer to 3 decimel places.) c. Compute the value of the test statistic. (Round your answer to 3 decimal places.) d. What is your decision regarding the null hypothesis? Use the 0.025 significance level

Answer 1

The student is conducting a right-tailed hypothesis test with unequal variances for two sample means. Steps include setting up hypotheses, calculating degrees of freedom, stating the decision rule, finding the test statistic, and deciding whether to reject the null hypothesis based on critical values from the t-distribution.

Step-by-step explanation:

The student is asking how to conduct a hypothesis test comparing two sample means with unequal variances at a significance level of 0.025.

Steps for Hypothesis Testing

Set up the null and alternative hypotheses. In this case:
H0: μ1 ≤ μ2 (Null Hypothesis)H1: μ1 > μ2 (Alternative Hypothesis) - This is a right-tailed test.

Calculate the degrees of freedom (df) using the formula for unequal variances. However, to do this calculation, you need both sample sizes and standard deviations, which we have. Since this information is given in detail in the question, we can compute the df accurately.

State the decision rule based on the significance level given (α = 0.025). You will use the t-distribution table to determine the critical value.Calculate the test statistic using the formula for two independent samples with unequal variances.

Based on the calculated test statistic and the critical value derived from the t-distribution table, decide whether to reject or not reject the null hypothesis.If the test statistic exceeds the critical value, we reject the null hypothesis; if not, we fail to reject it.