This assignment consists of 5 questions (Answer all questions)
(Due on 28 October 2005 by 5pm)
Question 1 (20 Marks)
(a)Households in a certain city were surveyed to determine whether they would or would not subscribe to a cable television service. The households were classified as “low,” “meddle,” or “high” income. The below gives the proportions of households in each of the six joint classifications.
|Income |Subscribe | | |Yes |No | |Low |0.03 |0.17 | |Middle |0.14 |0.46 | |High |0.10 |0.10 |
i) Find the probability that a randomly chosen household would subscribe ii) Are income and willingness to subscribe independent? iii) Given that a high-income family has been contacted, find the probability that the household will subscribe.
(b) The information that follows shows the distribution of the number of days of sick leave taken by 200 employees during a year:
|Days |0 |1 |2 |3 |4 |5 |6 |7 | |Number of employees |20 |40 |40 |30 |20 |10 |10 |30 |
Let X denote the number of days of sick leave taken by an employee.
Find (i) [pic]; (ii) [pic]; (iii) [pic]); (iv) [pic]
Question 2 (20 Marks)
An executive fot Tri-State Coal Incorporated wants to determine the average amount of coal mined per day by miners in a certain mine. A random sample of 10 miners produces the following tonnages of coal on a certain day:
Based on the sample information answer the following questions:
i) Find a 90% confidence interval for the mean tonnage
ii) Find a 95% confidence interval for the mean tonnage State all necessary assumptions for the interval to be operational.
Question 3 (20 Marks)
a) The Douglas Drug Company claims that its medication takes effect within 12 minutes. The following data show the times that 10 patients required before feeling the effects of the medication:
8.1, 11.6, 9.4, 13.3, 16.2, 10.3, 14.6, 15.3, 13.6, 15.2
Use a 5% level of significance and test [pic] minutes against [pic] minutes. State all necessary assumptions for the test to be operational.. b) An economist claims that the unemployment rate for non-English-speaking individuals in New York City is at least 30%. In a random sample of 400 non-English –speaking residents of New York City, 90 are unemployed. i) Calculate the sample proportion who are unemployed. ii) Test [pic] against [pic] using 5% level of significance.
Question 4 (20 Marks)
a) A standard argument of students in all universities is that grades in certain departments tend to be higher or lower than grades in other departments. Test this claim, samples of grades from three departments were obtained. Students’ grades were distributed as follows:
|Department |Grade | | |A |B |C |D |F | |Math |50 |140 |200 |180 |20 |...