Final answer:
To ascertain if there's a significant difference in processing speed between Program A and Program B, we conduct a hypothesis test for two independent means at a 0.05 significance level, calculate the test statistic, and interpret the p-value to reject or fail to reject the null hypothesis.
Step-by-step explanation:
The Simone Company's consideration of two different computer programs to speed up inventory processing involves comparing the means of two independent samples. With 25 employees testing each program, we have Program A with a mean processing time of 30 seconds and Program B with a mean processing time of 28 seconds.
We also know the standard deviations for each program's processing times: 5 seconds for Program A and 3 seconds for Program B.
To determine if there is a significant difference between Program A and Program B, we will conduct a hypothesis test for two independent means. To start, we might choose a common significance level such as 0.05 (5%).
The null hypothesis (ₓ₀) is that there is no difference in the means of the two programs' processing times, while the alternative hypothesis (ₓ₁) is that there is a difference.
When calculating the p-value, we use the mean, standard deviation, and sample size of both groups to find the test statistic, which follows a t-distribution, because we are assuming we do not know the population standard deviation.
Afterward, we'll compare this test statistic to the critical value or check the p-value to decide whether or not to reject the null hypothesis.
Interpretation of a p-value involves comparing it to the chosen significance level. If the p-value is less than the significance level, we reject the null hypothesis, indicating that there is a statistically significant difference between the processing times of the two programs.
However, if the p-value is greater, we fail to reject the null hypothesis, suggesting that any observed difference in processing times could be due to chance.