Business Statistics Homework

Answer statistical calculation questions with steps and essay questions with key points. SCENARIO: The University of La Verne want to find out how many jobs offers its undergraduate and graduate business alumni have gotten upon graduation and what their salaries are now. 1. The following table lists the number alumni have and have not gotten job offers around graduation by major (20 points, each 5 points, Review PPT page 7). Accounting Finance Management Supply Chain Yes 15 25 30 20 No 5 10 20 25 (a). What is the probability of selecting a graduate whose major is management and does have job offer? (b). If a graduate selected is supply chain major, what is the probability that the graduate has no offer? (c). What is the probability of selecting a finance major graduate? (d). What is the probability that you select a graduate who either majors in accounting or has job offer? 2. The following table lists the total number of alumni by the number of job offers they have gotten around graduation (10 points, 5 points each, Review PPT page 10). # of Job Offer/X Total # of Alumni 0 25 1 55 2 45 3 40 4 or more 35 (a) What is the probability that a graduate has 1 or fewer job offer? (b) What is the probability that a graduate has 3 or more job offers? 3. The alumni responded that it took about 15 to 55 days to get the first offer. Supposed the time needed to get the first offer is a uniform probability distribution. Please calculate (20 points, 10 points each, Review PPT page 13-15). (a) The probability of taking the alumni to get their first offer for fewer than 30 days. (b) The probability of taking the alumni to get their first offer between 20-50 days. 4. The dean has observed for several years and found that the probability distribution of the salary of the alumni’s first job after graduation is normal, with a mean of $55k per year and a standard deviation of $5k (30 points, 10 points each, Review PPT page 16-25): (a) What’s the probability that the alumni get a salary of $50k or more in their first jobs? (b) What’s the chance that the alumni get a salary between $40k and $60k? (c) What is the salary range that 95% of the alumni should be belonged to? 5. Suppose the distribution of alumni salary has a mean of $55k per year and a standard deviation of $5k. The research office collected salary information from 121 business alumni. Its collected data show that the mean salary of their first job is $58k per year (20 points, 10 points each, Review PPT page 27-29. (a) What is the sample size and standard error of the data collected? (b) What is the probability that the sampled alumni have a mean salary of $58k or more? ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Question 1-5 (100 points): The dean of the College of Business at the University of La Verne has observed for several years and found that the probability distribution of the salary of the alumni’s first job after graduation is normal. The college collected information from 1000 alumni and finds that the mean of their salary is $50k. Assuming a 95% confidence level, please do the following 1. Suppose the dean believes that the average salary of the population should be about $55k per year, with a standard deviation of $10k. We need to conclude that the mean salary is less than what the dean has believed to be (30points, Review PPT Chapter 10). (Hint: Hypothesis Testing and Confidence Interval - One sample; population standard deviation is known) (a) What are the null and alternate hypotheses (5 points)? (b) What is the level of significance (5 points)? (c) What is the standard error (5points)? (d) Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic) (10 points)? (e) What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule (5 points). 2.Suppose the population standard deviation of $9k (20points, Review PPT Chapter 9): (Hint: Hypothesis Testing and Confidence Interval - One sample; population standard deviation is known) (a) What is the Z critical value of 95% confidence interval (5 points)? (b) What is the standard error (5points)? (c) Please estimate the confidence interval of the population’s average salary (hint: write down the equation and calculate the results) (10 points) 3.Suppose the standard deviation of the collected data from 1000 alumni is $10k. Can we conclude that the true mean of alumni salary is different from $55 (20 points; Review PPT Chapter 10)? (Hint: Hypothesis Testing and Confidence Interval - One sample; sample standard deviation is known) (a) What are the null and alternate hypotheses (5 points)? (b) Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic, 10 points). (c) Please make the conclusion (5 points). 4.Suppose that the standard deviation of the collected data from 1000 alumni is $10k and the mean is $50k, please estimate the confidence interval of the population’s average salary (10 points, Review PPT Chapter 9). (Hint: Hypothesis Testing and Confidence Interval - One sample; sample standard deviation is known) 5.The dean wants to know whether there is salary difference between male and female alumni. He knows that the population standard deviation for male is $8 and for female is $10. The sampled data show that the average salary for 100 male is $56 and the average salary for 121 female is $52 (20 points, Review PPT Chapter 11). (Hint: Hypothesis Testing and Confidence Interval - two samples; population standard deviation is known) (a) What are the null and alternate hypotheses (5 points)? (b) Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic) (10 points)? (c) What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule (5 points).