1. A company decides to add a new program that prepares randomly selected sales personnel to increase their number of sales per month. The mean number of sales per month for the overall population of sales people at this national company is 25 with a standard deviation of 4. The mean number of sales per month for those who participated in the new program was 29.
I'm not sure what you might be asking.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To determine the effectiveness of the new program, we can use hypothesis testing to compare the mean number of sales per month for those who participated in the program (29) with the overall population mean (25). Here are the steps to perform the hypothesis test:
1. Set up the null hypothesis (H0) and alternative hypothesis (Ha):
- Null hypothesis (H0): The mean number of sales per month for those who participated in the program is equal to the overall population mean (μ = 25).
- Alternative hypothesis (Ha): The mean number of sales per month for those who participated in the program is greater than the overall population mean (μ > 25).
2. Determine the significance level (α) for the hypothesis test. This is the maximum probability of rejecting the null hypothesis when it is true. For example, if α = 0.05, it means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).
3. Collect a sample of data from those who participated in the program and calculate the sample mean (ȳ) and sample standard deviation (s).
4. Calculate the test statistic using the formula:
- t = (ȳ - μ) / (s / √n)
where ȳ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
5. Determine the critical value or p-value for the test statistic. This depends on the significance level (α) and the alternative hypothesis. If using a t-distribution, you can find the critical value from the t-table, or use statistical software to calculate the p-value.
6. Compare the test statistic with the critical value or p-value.
- If the test statistic is greater than the critical value or the p-value is less than α, reject the null hypothesis. This means there is evidence to support the alternative hypothesis.
- If the test statistic is less than the critical value or the p-value is greater than α, fail to reject the null hypothesis. This means there is not enough evidence to support the alternative hypothesis.
Remember to interpret the results in the context of the question. In this case, if the null hypothesis is rejected, it would indicate that the program has a statistically significant effect on increasing the number of sales per month for the sales personnel.