Discuss the below:
Q1: Hypothesis Tests on two populations
The Management of Discount furniture designed an incentive plan for its Salespeople.To evaluate this innovative plan, 12 sales persons were selected at random and their weekly sales before and after the plan were recorded. The paired data is:
Before: 408, 377, 506, 518, 319, 408, 552, 658, 350, 420, 514, 413
After: 485, 409, 577, 541, 298, 517, 637, 592, 447, 459, 558, 489
At a 10% level of significance, was there a significant increase in the typical salesperson's average weekly income due to innovative incentive plan? If the null hypothesis is rejected, give the p-value and interpret it.
Q2: Hypothesis Tests on two populations
A research organization conducted identical surveys in 1995 and 2005. One question asked women was: "Are most men basically kind, gentle and thoughtful?" The 1995 survey revealed that , of the 3000 women surveyed, 2252 said that they were. In 2005, 1740 of the 3200 women surveyed said that they were. At the 0.05 level can we conclude that women think that men are less kind, gentle and thoughtful in 2005 compared to 1995? If the null hypothesis is rejected, give the p-value and explain what it means.
Q3: Hypothesis Tests on two populations
Rates of return (annualized) in two investment portfolios are compared over the last 12 quarters. They are considered similar in safety, but portfolio B is advertised as being "less volatile". At a significance level of 0.05, does the sample below show that portfolio A has significantly different variance in rates of return than portfolio B?
Portfolio A: 4.83 10.52 12.65 5.22 6.55 8.67
(rates of return) 7.88 9.19 9.77 3.48 9.65 10.29
Portfolio B: 5.96 8.16 7.75 10.89 9.46 10.45
(rates of return) 6.76 8.36 8.56 8.97 7.91 8.61