Statistics and Probability Answers

For a set of data, the coefficient of correlation is r=0.57 and the variable X and Y are directly related. The coefficient of determination is r equal to
1. 0,75
2. 0,57
3. 0,32
4. 0,49
5. 0,67

In testing the independent of two variables described in a contingency table, the critical value a chi-square it the test is to be conducted at the level of significance a=0,05 and the degrees of freedom df= 5 is
1. 0,412
2. 9, 236
3. 16,750
4. 15,086
5. 11,071

Let X=level of income and Y=political preference. Use the results shown in the table below abd test on a1% level of significance whether the political preference and the level of income are independent
Political party: Level of income A - 23, 40, 16, 2
B - 11, 75, 107, 14
C - 1, 31, 60, 10
Suppose that the test statistic calculated is 69, 3875, which statement is incorrect?
1. H0 The variable are independent
H1 The variables are dependent
2. The degrees of freedom df = 12
3. The critical value =16, 812
4. There are 390 people
5 H0 is rejected The two variable are dependent

Consider the following hypothesis test
H0 u=50 vs H1 u>50
A sample of 60 is used and the population standard deviation a is 8 when X=52,5. The p-value is
1. 2,4206
2. 0,0078
3. 0,0156
4. 0,9922
5. 0,9918

A simple random sample of 40 0 individuals provides 100 yes responses . The 95% confidence interval for the population proportion is
1. (0,165 ; 0.335)
2. (0,516 ; 0.535)
3. (0,156 ; 0,335)
4. (0,25; 0,085)
5. (0,2075 ; 0,2925)

A simple random sample of 40 items results in a sample mean of 25 . The population standard deviation is a=5 . The 95% confidence interval of the population mean is
1. (25 ; 1,5495)
2. (23,4006 ; 26,5993)
3. (23,4505 ; 26,5495)
4. (23,6679 ; 26,3321)
5. (25,516 ; 27,4591)

QUESTION 4 (10 MARKS)



The asset turnovers, excluding cash and short-term investments, for the Blue Waters Fishing Company from 2010 to 2019 are listed below (in $mil):







YEAR

2010

2011

2012

2013

2014

2015

2016

2017

2018

2019

TURNOVERSS

3.0

4.2

4.8

3.7

3.4

4.3

5.6

4.4

3.8

4.1





4.1 Determine the least squares trend line equation, using the sequential coding method with X=1 in 2010 (6)



4.2 Use the trend line equation to estimate turnovers for 2008 and 2022. (2 x 2 = 4)

QUESTION 3 (13 MARKS)

A faculty is interested in whether there is a relationship between gender and favourite subject at his college students. He tabulated some men and women on campus and asked them if their favourite subject was Mathematics (M), Geography (G), and Science (S).

M

G

S

Total

Women

10

14

10

34

Men

11

22

14

23

Total

21

36

24

57



Use the data provided above to test if there is any relationship between gender and favourite subject. By using α = 0.01, Answer the following questions

3.1) Formulate the null and alternative hypotheses (2)

3.2) Select and compute the test statistic(5)

3.3) Obtain the critical value and formulate the decision.(3)

3.4) Based on the information obtained in Questions 3.1 ; 3.2 & 3.3, what can the faculty conclude? (3)

QUESTION 2 (13 MARKS)

A manufacturer claims that the percentage of faulty items in any lot of the articles he produces is 1%. A random sample of 200 articles is selected and 8 are found to be faulty.

To test the validity of this claim, and using α = 0.01, Answer the following questions

2.1) Formulate the null and alternative hypotheses (2)

2.2) Select and compute the test statistic (4)

2.3) Obtain the critical value and formulate the decision. (4)

2.4) Based on the information obtained in Questions 2.1 ; 2.2 & 2.3, what can you say about the manufacturer’s claim ? (3)

QUESTION 1 (14 MARKS)

A specific task in a factory takes 5 minutes in average to be completed. The factory manager believes that the workers spend more time in this operation. The manager selects a sample of 11 timings for this worker and collects the following data (in minutes): 4.8 ; 5.6 ; 5.3 ; 5.2 ; 4.9 ; 4.7 ; 5.7 ; 4.9 ; 5.7 ; 4.9 ; 4.6.

To test the validity of this factory manager’s belief, and using α = 0.05, Answer the following questions

1.1) Formulate the null and alternative hypotheses (2)

1.2) Select and compute the test statistic (6)

1.3) Obtain the critical value and formulate the decision. (3)

1.4) Based on the information obtained in Questions 1.1 ; 1.2 & 1.3, what can you say about the manager’s belief ? (3)