1. The Dean of SASTE wants to know which batch of Education students performed better in English. He took a random sample of 40 Education students in last year's batch and found it to have a mean final grade of 83 with a standard deviation of 7. Fifty Education students from this year's batch were randomly taken and it was found that they have a mean final grade of 86 with a standard deviation of 10. Compute the Z-test.
2. In the previous problem, does the indicate that last year's batch is poorer in English than this year's batch? Consider the Ho and Ha statements below: Ho: Last year's batch is as good as this year's batch in English. Ha: Last year's batch is poorer in English than this year's batch. NOTE: Test at = 0.01. (Hint: Use the 5-step solution of Testing Hypothesis)
3. A budget head for SSS Sales Inc. would like to compare the daily travel expenses for the sales staff and the audit staff. He collected the following sample information: [Sales Staff: 105; 120; 140; 160; 100; 170; 160; 140; 130; 160; 180; 190] [Audit Staff: 130, 50; 90; 80; 70; 125; 180; 80; 110] At 0.05 significance level, can be conclude that the men daily expenses of sales staff are greater than the audit staff? What is the degree of freedom of the given problem?
4. A budget head for SSS Sales Inc. would like to compare the daily travel expenses for the sales staff and the audit staff. He collected the following sample information: [Sales Staff: 105; 120; 140; 160; 100; 170; 160; 140; 130; 160; 180; 190] [Audit Staff: 130, 50; 90; 80; 70; 125; 180; 80; 110] At 0.05 significance level, can be conclude that the men daily expenses of sales staff are greater than the audit staff? Calculate the t-value.
5. The owner of a chain of fruit shake stores would like to study the correlation between atmosphere temperature and sales during the summer season. A random sample of 12 days is selected with the results given as follows: {Temperature (0F): 79; 76; 78; 84; 90; 83; 93; 94; 97; 85; 88; 82} {Total Sales: 147; 143; 147; 168; 206; 155; 192; 211; 209; 187; 200; 150} At 0.05 significance level, can we conclude that there is a significant correlation between the atmospheric temperature and total sales of fruit shake? Compute for the value of Spearman Rank Order Correlation.