MGT4701

Advanced Business

Statistics Summer 2024

Group Assignment 1

1    Battery manufacturers compete on the basis of the amount of time their products last in cameras and toys. A manufacturer of alkaline batteries has observed that its batteries last for an average of 6.9 hours when used in a toy racing car. The amount of time is normally distributed with a standard deviation of 2.1 hours.

a.   What is the probability that the battery lasts between 6 and 8 hours?

b.   What is the probability that the battery lasts longer than 7 hours?

c.   What is the probability that the battery lasts less than 4 hours?

d.   What is the amount of time below which only 10% of all a battery lasts?

2    The employee database show City, Gender, Age, and Salary of 340 samples  from  a  car manufacture company employee.

a.   With  95% confidence level, estimate the average salary of men in city A. Repeat your calculation for women in city C.

b.   Regardless of which city they are working, suppose you want to estimate the average salary of men within 210 units with 99% confidence level. According to historical data you know the standard deviation of the salary is 5000. What sample size would be required?

c.   Estimate with 95% confidence the difference population mean of men and women’s salary in city A.

3    Refer to the employee database in question 2.

a.   With 95% confidence level, can we conclude that the average salary of men in city A is higher than average salary of men in city C?

b.   Test whether there is sufficient evidence to show that the average age in men group is equal to women (regardless of which city they are working). Assume 90% confidence level.

c.   Are you agreed with this statement; “in city B, women employees are younger than men”? Use 99% confidence level.

4    Refer to the Govern2014 database answer following questions (use 99% confidence level):

a.   In recent years, women have made up an increasing proportion of university students. Is there sufficient evidence to conclude that females and males (Sex: 1 = male, 2 = Female) differ in their years of education (EDUC)?

b.   Men are often accused of spending too much time watching television. However, do men watch more TV than women (Sex: 1 = male, 2 = Female)? Conduct a test to answer this question (TVHOURS)

5    California university is investigating expanding its evening programs. It wants to target people between 25 and 55 years old who have completed high school but did not complete college or university. To help determine the extent and type of offerings, the university needs to know the size of its target market. A survey of 320 California adults was drawn and each person was asked to identify his/her highest educational attainment. The responses are:

1.   Did not complete high school

2.   Complete high school

3.   Some college or university

4.   College or university graduate

Also, each person was asked whether he/she had plans in the next 2 years to take a course (1 = No and 2 = Yes). With 1% significance level, can we conclude that Californians who did not complete high school are more likely to take a course in the university’s evening program?

6    In a large production plant, the operations manager wants to estimate the average amount of time workers take to assemble a new computer keyboard. She observed a number of workers assembling similar keyboards. She guesses that the standard deviation is 6 minutes. With 90% confidence level, if she wishes to estimate the mean assembly time to within 25 seconds, how large a sample of workers should she take?

7    A  TV producer company wants to determine the number of hours that people  spend  on watching training programs. The company hired a statistician to survey 151 randomly selected homes and determined the number of hours. (refer to the Excel file for data, TV Producer). Estimate with 90% confidence the average hours that people spend on watching training programs.

8    In one survey, about project managers’ educational background, 390 operation managers of medium and large construction companies were selected and asked about their degrees. There were  108 PMPs. Estimate with 95% confidence the proportion of all project managers of medium and large construction companies who have PMPs.