1. When using independent samples to test the difference between two population means, a pooled variance is used if the population variances are unknown and assumed unequal (5 points).

TrueFalse

2.When doing a two sample test of proportions, assuming the sample is <10% of the population and np>10 and n(1-p)>10, we calculate a z statistic which follows a standard normal distributions (5 points)

TrueFalse

3.Random samples of students were compared to see whether or not there was a difference in the proportion favoring the university's proposed switch from MWF (three-day) classes to MW and TR (two-day) classes. In the resident population 97 out of 200 favored the switch.In the commuter population, 114 out of 200 favored the switch.Conduct a hypothesis test at the .05 significance level to see if there is a difference in the proportion of residents and commuters who prefer the switch (10 points).

For the following please use the dataset called "sales.xlsx".

You work for a busy internet retailer and are trying to optimize the feel and layout of the company's website.There are over 2 million site visitors per year. In the dataset titled "sales.xlsx" there are two columns of information. The first is a list of purchase amount by visitor using website layout 1 (called Light and Breezy). The second is a list of purchase amounts by site visitors using website layout 2 (called Aggressive). For a short period, site visitors were randomly routed to one of the two layouts. Using the data in the file "sales.xlsx", please answer the following questions (when required make sure to perform all steps of the hypothesis test):

Note 1: The column "PA: Light and Breezy" is a column of sales per visitor for the "Light and Breezy" layout.

Note 2: The column "PA: Aggressive" is a column of purchase amount per visitor for the "Aggressive" layout.

Note 3: Each row represents one visitor to each site (not the same visitor going to each site). Visitors were randomly directed to each layout, but overall sample size is still a little different.During the test, 770 visitors were sent to the "Light and Breezy" layout while 742 were sent to the "Aggressive"

4.Is there a difference in the proportion of site visitors that make a purchase (any customer with a sales amount > 0 made a purchase, any customer with a sales amount = 0 did not) between the two layouts at the .05 significance (20 points)?

5.Of the visitors who made a purchase, is there a difference in the average amount purchased by visitors to each site layout? Perform a hypothesis test at the .05 significance. (20 points)

6.Does the "Aggressive" layout increase average amount purchased by visitors who make a purchase? Perform a hypothesis test at the .05 level. (20 points)

7.Your new boss is particularly fond of the Aggressive layout.She believes that "in your face" product placement and descriptions work the best.Based on your analysis so far, write a short description that supports or refutes her perspective on the aggressive layout. Please provide specific evidence for your conclusions (20 points).