Question

A national firm reports mean earnings of $75 ± $12 (µ ± σ) per unit sold over the lifetime of the company. A competing company over the past 36 reporting periods had reported mean earnings equal to $78 per unit sold. Conduct a one-sample z test to determine whether mean earnings (in dollars per unit) are larger (compared to that reported by the national firm) at a .05 level of significance.

1.State the value of the test statistic and whether to retain or reject the null hypothesis.
2.Compute effect size using Cohen’s d.

Answer 1

To conduct a one-sample z test, we state the null and alternative hypotheses, calculate the test statistic and the p-value, compare the p-value to the significance level, and state the conclusion. The effect size can be computed using Cohen's d.

Step-by-step explanation:

To conduct a one-sample z test to determine whether the mean earnings are larger than that reported by the national firm, we can follow these steps:

1. State the null and alternative hypotheses: Null hypothesis (H0): The mean earnings are equal to $75. Alternative hypothesis (H1): The mean earnings are larger than $75.
2. Calculate the test statistic: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). In this case, z = (78 - 75) / (12 / sqrt(36)) = 3/2 = 1.5.
3. Find the p-value: Using the z-table or a calculator, we can find that the p-value associated with a z-score of 1.5 is approximately 0.9332.
4. Compare the p-value to the significance level: Since the p-value is greater than the significance level of 0.05, we do not have enough evidence to reject the null hypothesis.
5. State the conclusion: Based on the results of the test, we cannot conclude that the mean earnings are larger than that reported by the national firm.

To compute the effect size using Cohen's d, we can use the formula: d = (sample mean - population mean) / population standard deviation. In this case, d = (78 - 75) / 12 = 3/12 = 0.25. According to Cohen's standards, this would be considered a small effect size.