Step by step answer for the following questions.
Explain your answers including formulas. (Do not rely on built-in functions in Excel or other software.
In a situation similar to one you may have seen before, there is a clinic with two physicians, Dr. X and Dr. Y, and each doctor can be scheduled to see at most 3 patients per hour. The joint probability mass function is given by the following table. Assume we allow X and Y represent the random variables associated with the number of patients seen in a given hour by Drs. X and Y, respectively.
a.) What are mX and sX?
b.) What are mY and sY?
c.) What is E(XY)
d.) What is Cov(X,Y)?
e.) What is rX,Y?
f.) What does this value for rX,Y tell us about the relationship between the number of patients seen by the two doctors?
2. It is well established that your company's current hiking shoe design lasts on average 900 miles. It is also well known that the durability of hiking shoes is normally distributed. By adding a new ingredient to the soles, you believe you can extend the life. But you want a small test of ten pairs of shoes to make it quite clear this is true before proposing extensive testing. The durability results in miles for the 10 pairs are 951, 1039, 758, 1110, 957, 1014, 1273, 1004, 853, and 1072.
a.) State the situation as a hypothesis testing problem
b.) Show in detail how to calculate the sample standard deviation.
c.) With significance level a = 0.05 would you reject the null hypothesis? Explain clearly why or why not.
d.) What is the P-value for this situation?
3. You want to attempt to direct market magazine subscriptions only if there is strong evidence that more than 10% of potential customers would respond. If for a sample mailing to160 potential customer, 23 of these responded:
a.) Express the situation as a hypothesis testing problem
b.) If you were to use an a = 0.01 significance level what would you do in the circumstances given? Explain clearly why or why not