SALES represent the number sales made this week.
CALLS represent the number of sales calls made this week.
TIME represents the average time per call this week.
YEARS represents years of experience in the call center.
TYPE represents the type of training the employee received.
- Hypothesis Testing and confidence intervals
Complete the following four hypotheses, using ? = 0.05 for each.
a. Mean sales per week exceeds 41.5 per salesperson
b. Proportion receiving online training is less than 55%
c. Mean calls made among those with no training is less than 145
d. Mean time per call is greater than 15 minutes
1. Using the data set, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager''s belief. Use the Seven Elements of a Test of Hypothesis (1. the null hypothesis, 2. The alternative or research hypothesis, 3. Test statistic, 4. Rejection region, 5. Assumptions, 6. Experiment and calculation of test statistic, 7. Conclusion) as well at the p-value calculation and explain your conclusion in simple terms.
2. Compute 99% confidence intervals for each of the variables described in a.-d., and interpret these intervals.
3. Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.
- Regression and Correlation Analysis
Use the dependent variable (labeled Y) and one of the independent variables (labeled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following.
1. Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the "best fit" line. Interpret.
2. Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.
3. Determine the coefficient of correlation. Interpret.
4. Determine the coefficient of determination. Interpret.
5. Test the utility of this regression model, represented by a hypothesis test of b=0 using ?=0.10. Interpret results, including the p-value.
6. Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable?
7. Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.
8. Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval.
9. Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval.
10. What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.
Summarize your results from Steps 1-10 in a 3-page report. The report should explain and interpret the results in ways that are understandable to someone who does not know statistics.
Attachment:- data set.xlsx