We shall consider the general method, employed by an adversary,  to prove that no algorithm can always decide a given problem X using less than M questions. For that purpose, the adversary maintains Q, and R_1 … R_M, such that : 1. X(Q) is false2. X(R_i) is true for all i \in 1 … M and such that after k questions from the algorithm:3. Q is consistent with all k answers from the adversary 4. for all i in 1 … M, except for at most k such, it holds that R_i is consistent with all k answers from the adversary.For each declaration from the algorithm, how should the adversary respond?

What is the average probability of purchase for all people that come to the website (independent of the specific landing page)?

A company is interested in understanding the factors that drive purchase on their website.  They ran a test where they collected data from 2500 visitors to their website and observed if a purchase was made or not.  This analysis includes the following variables:  Customer ID: Unique identifier for each customer Purchase: 1 = purchased; 0 = did not purchase Female: 1 = Female; 0 = Male Paid Ad: 1 = Arrived on webpage via a paid advertisement; 0 = came from somewhere else Urban: 1 = livesin an urban location; 0 = does not To understand the relationship between these variables and purchase they ran a regression where “Purchase” was the dependent variable.  Results appear in the table below.  Use these results to answer the following questions: By how much does the probability of purchase change if the individual is female? 

What the the EMV for this customer?  

What is the problem with this survey question? “How effectively has your organization leveraged Kubernetes for container orchestration and CI/CD pipeline optimization?”  

he results of the statistical test appear in the following table: At an alpha level of 0.05, what do you conclude from this test?  

If a customer makes a purchase, what is the probability that they came from Landing Page A?

What is the average probability of purchase for all people that come to the website (independent of the specific landing page)?

To test this hypothesis, the company ran an experiment where they filtered 3000 individuals to the new landing page and recorded how many made a purchase.  The also recorded the average $ spend for each transaction and the corresponding standard deviation.  The results of this experiment appear in the table below:    # Visitors # Purchased % Purchased Avg. $ Spend Standard Deviation $ Spend 3000 105 3.5% $121.34 $21.30   What is the mathematical difference between the observed and hypothesized conversion rates?

By how much would Unit Sales change if our competitor raised their price by $1.25?