Week 5 Homework: Lisa Monnin And The Budget

Week 5 Homework Homework #1ms Lisa Monnin Is The Budget

Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information. Sales ($) Audit ($) At the 0.1 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? (a) State the decision rule. (Round your answer to 3 decimal places.) Reject H₀ if t > (b) Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.) Pooled variance (c) Compute the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic (d) State your decision about the null hypothesis. H₀: μ_s ≤ μ_a (e) Estimate the p-value. (Round your answers to 3 decimal places.) p-value

Paper For Above instruction

In this analysis, we examine whether there is a statistically significant difference in the mean daily travel expenses between sales and audit staff at Nexus Media Inc., utilizing a two-sample t-test for independent samples. The significance level is set at 0.1 to determine if the mean expenses for sales staff are greater than those for audit staff.

First, the null hypothesis (H₀) posits that the mean expenses are less than or equal (μ_s ≤ μ_a), while the alternative hypothesis (H₁) suggests that the mean expenses for sales staff exceed those for audit staff (μ_s > μ_a). The decision rule involves calculating the test statistic and comparing it to the critical t-value for a one-tailed test at the 0.1 significance level.

To perform the hypothesis testing, the pooled estimate of the population variance is calculated from the sample data. Assuming the sample variances are similar, the pooled variance is determined by combining the sum of squared deviations weighted by their degrees of freedom, divided by the total degrees of freedom. This value provides an estimate of the common population variance under the assumption of equal variances.

The test statistic is computed using the difference between the sample means divided by the standard error of the difference, which incorporates the pooled variance and the sample sizes. The formula is:

t = (mean_sales - mean_audit) / sqrt( pooled variance * (1/n_sales + 1/n_audit) )

The computed t-value is then compared to the critical value from the t-distribution with the combined degrees of freedom to determine whether to reject the null hypothesis. If the test statistic exceeds the critical value, we reject H₀.

Finally, the p-value corresponding to the computed test statistic is estimated to quantify the probability of observing such a difference if the null hypothesis were true. A p-value less than the significance level supports rejecting the null hypothesis, indicating a statistically significant greater mean expense for sales staff.

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