math : Solution Essays

1)  A light bulb producing company states that its lights will last an average of 1200 hours with a standard deviation of 200 hours.  A sample of 100 light bulbs from the company were tested and the researcher found that the average life of each light bulb was 1050 hours.  At a 95% confidence level, determine whether these light bulbs are in compliance with the company’s claim.

2)  A company’s human resource department claims that all employees are present on the average 4 days out of the work week with a standard deviation of 1.  They hired an outside company to do an audit of their employees’ absences.  The company took a sample a 10 people and found that on the average the employees were present 3 days per week.  With a 95% confidence level, determine whether the company’s claim is true based on the data from the sample.

3)  A teacher claims that all of her students pass the state mandated test with an average of 90 with a standard deviation of  10.  The principal gave the test to 20 of her students to see if the teacher’s claim was true.  He found that the average score was 75.  With a 95% confidence level, determine whether the teacher is making the correct claim about all of her students.

4)  The lifeguard’s at a local pool have to be able to respond to a distressed swimmer at an average of 10 seconds with a standard deviation of 4 in order to be considered for employment.  If a sample of 100 lifeguards showed that their average response time is 15 seconds, with a confidence level of 95% determine whether this group may be considered for employment.

5)  It is believed that an average of  20 mg of iodine is in each antibiotic cream produced by a certain company with a standard deviation of 5 mg.  The company pulled 150 of its antibiotic creams and found that on the average each cream contained 29 mg of iodine.  Determine with a 95% confidence level whether or not these creams are in compliance with the company’s belief?

For questions 6 – 10 use the chi-squared distribution to test the hypothesis.

6)  A restaurant owner wants to see if the business is good enough for him to purchase a restaurant.  He asks the present owner for a breakdown of how many customers that come in for lunch each day and the results are as follows:  Monday – 20, Tuesday – 30, Wednesday – 25, Thursday – 40 and Friday – 55.  The prospective owner observes the restaurant and finds the following number of customers coming for lunch each day:  Monday- 30, Tuesday – 15, Wednesday- 7, Thursday 40, and Friday – 33.  At a 95% confidence level determine whether the present owner reported the correct number of customers for lunch each day.

7)  An employer polled its employers to see if they agree with the proposed new store hours and whether or not their present shift made a difference in their answers.  The customers answered 1 for agree, 2 for don’t know, and 3 for disagree.  Nine first shift employees answered “agree”, 15 second shift employees answered “agree”, and 20 third shift employees answered agree.  With a 95% confidence level determine whether or not the employees’ present shift played a role in their responses to the poll.

8)  A politician surveyed 100 citizens to determine if their job title had anything to do with the way they responded to the following statement:  “A city-wide curfew will be put into place.  Select the time that you think it should be put into place.  8pm, 9pm, or 10pm”.  He is mostly concerned with the 10 pm responses.  25 teachers chose 10pm, 40 doctors chose 10pm, and 35 police responded 10pm.  With a 95% confidence level, determine whether job title plays a role in how the citizens responded to the statement.

9)  A meter reader did an experiment to see if there is a relationship between the number of tickets she writes and the number of blocks she is away from the park that is considered the heart of the city.  At 0 blocks from the park she writes 35 tickets, at 1 block away from the park she writes 25 tickets, at 2 blocks from the park she writes 20 tickets and at 3 blocks from the park she writes 25 tickets.  Use a 95% confidence level.

10)  A high school principal asks his students to respond to the following statement:  “School should start at 9:00am rather than 7:00am.  Answer 1 for agree, 2 for don’t know, and 3 for disagree.”  There were 90 seniors who answered agree, 35 juniors, 30 sophomores, and 25 freshmen.  Help the principal decide with a 95% confidence level that the students’ status played a role in how they responded to the question.