Statistics for Business: Covariance, Correlation, and Hypothesis Test

This assignment provides detailed solutions to statistical problems, covering covariance and correlation analysis, exponential distribution calculations, and hypothesis testing. The first question involves calculating and interpreting covariance and correlation between two variables, explaining the possible reasons for negative relationships. The second question focuses on the exponential distribution, determining the proportion of customers who abandon calls after a certain hold time, finding the waiting time threshold, and calculating probabilities for specific hold time intervals. The third question addresses hypothesis testing, calculating the probability of type II error and the power of the test, interpreting the meaning of the test's power, and reviewing the impact of sample size on the significance level. The final question involves hypothesis testing regarding filling weights, comparing the computed z-value with the critical z-value to determine whether to reject the null hypothesis. Desklib provides access to more solved assignments and study resources for students.

Statistics for Business
Student Name:
Instructor Name:
Course Number:
30 September 2018

Question 1:
a) Calculate and interpret the covariance between x and y
Answer
5 20 -0.5 1.5 -0.75
3 23 -2.5 4.5 -11.25
7 15 1.5 -3.5 -5.25
9 11 3.5 -7.5 -26.25
2 27 -3.5 8.5 -29.75
4 21 -1.5 2.5 -3.75
6 17 0.5 -1.5 -0.75
8 14 2.5 -4.5 -11.25
b) Give a possible reason that the covariance is negative
Answer
The variables are negatively related hence the possible reason for the negative covariance
c) Calculate the coefficient of correlation, and comment on the relationship between x and y
Answer
5 20 100 25 400
3 23 69 9 529
7 15 105 49 225
9 11 99 81 121
2 27 54 4 729
4 21 84 16 441

6 17 102 36 289
8 14 112 64 196
= 44 = 148 = 725 = 284 = 2930
d) Give a possible reason that the correlation is negative
Answer
The variables are negatively related hence the possible reason for the negative correlation
Question 2:
a) What is the value of , the parameter of the exponential distribution in this situation?
Answer
b) What proportion of customers having to hold more than 1.5 minutes will hang up before
placing an order?
Answer
Thus 60.65% of customers having to hold more than 1.5 minutes will hang up before
placing an order.
c) Find the waiting time at which only 10% of the customers will continue to hold

Answer
d) What is the probability that a randomly selected caller is placed on hold for 3 to 6
minutes?
Answer
Question 3:
a) Calculate the probability of type II error when and α = 0.10.
Answer
We know
 This is a two-tailed test
 We will fail to reject the null (commit a Type II error) if we get a Z statistic
greater than -1.645.
 This -1.645 Z-critical value corresponds to some X critical value ( X critical),
such that

OR
Standardizing
Type II error is 0.3483.

b) Calculate the power of the test when and α = 0.10.
Answer
c) Interpret the meaning the power of the test.
Answer
The statistical power is given as 0.6517, this implies that the likelihood that a study will
detect an effect when there is an effect there to be detected is simply 0.6517.
d) Review the results of the previous questions. What is the effect of increasing the sample
size on the value of α?
Answer
When the sample size is increased, the value of also increases. However, an increase in
sample size results to a decrease in α.
Question 4
The critical z value is 1.96.
The computed z value is 1.6 and it is less than the critical z value hence we fail to reject
the null hypothesis. We therefore conclude that the filling weight is not 48.6 ounces but
rather 47 ounces.