Aptitude test on random sample

Assignment Help Basic Statistics
Reference no: EM131036376

1. The scores on an aptitude test required for entry into a certain job position have a mean of 500 and a standard deviation of 120. If a random sample of 36 applicants has a mean of 546, is there evidence that their mean score is different from the mean that is expected from all applicants?
(i) Do problem number 1 assuming that the sample size is 16.

2. The training department of a company wishes to determine if there is any difference in the performance between the workers that have completed a training program and those that have not completed the program. A sample of 100 trained workers reveals an average output of 74.3 parts per hour with a sample standard deviation of 16 parts per hour. A sample of 100 who have not been trained has an average output of 69.7 parts per hour with a standard deviation of 18 parts per hour. Is there evidence of a difference in output between the two groups? Write a 95% confidence interval estimate of the difference.

3. The manager of a consulting firm in Lansing, Michigan, is trying to assess the effectiveness of computer skills training given to all new entry-level professionals. In an effort to make such an assessment, he administers a computer skills test immediately before and after the training program to each of 20 randomly chosen employees. The pre-training and post-training scores of these 20 individuals are shown in the table below.

Employee

Score before

Score after

1

62

77

2

63

77

3

74

83

4

64

88

5

84

80

6

81

80

7

54

83

8

61

88

9

81

80

10

86

88

11

75

93

12

71

78

13

86

82

14

74

84

15

65

86

16

90

89

17

72

81

18

71

90

19

85

86

20

66

92

(i) Using a 10% level of significance, do the given sample data support that the firm's training programs is effective in increasing the new employee's working knowledge of computing?
(ii) Re-do using a 1% level of significance.

4. A marketing research consultant hired by Coca-Cola is interested in determining if the proportion of customers who prefer Coke to other brands is over 50%. A random sample of 200 consumers was selected from the market under investigation, 55% favored Coca-Cola over other brands. Additional information is presented below.
Sample proportion 0.55
Standard error of sample proportion 0.03518
Z test statistic 1.4213
p-value 0.07761

Sample proportion

0.55

Standard error of sample proportion

0.03518

Z test statistic

1.4213

p-value

0.07761

 

 

(i) If you were to conduct a hypothesis test to determine if greater than 50% of customers prefer Coca-Cola to other brands, would you conduct a one-tail or a two-tail hypothesis test? Explain your answer.
(ii) How many customers out of the 200 sampled must have favored Coke in this case?
(iii) Using a 5% significance level, can the marketing consultant conclude that the proportion of customers who prefer Coca-Cola exceeds 50%? Explain your answer.
(iv) If you were to use a 1% significance level, would the conclusion from part c change? Explain your answer.

5. The following table shows the Height (x) vs. Femur Length (y) measurements (both in inches) for 10 men:
Calculate the coefficient of correlation

x

70.8

66.2

71.7

68.7

67.6

69.2

66.5

67.2

68.3

65.6

y

42.5

40.2

44.4

42.8

40

47.3

43.4

40.1

42.1

36

6. Suppose a crime scene investigator digs up the femur of a man and finds that it is 38.5 inches long. Based on our regression line for the height vs. femur length data, what would we estimate the man's height to have been?
7. A researcher wants to know if there is a relationship between the number of shopping centers in a state and the retail sales (in billions $) of that state. A random sample of 8 states is listed below. After determining, via a scatter-plot, that the data followed a linear pattern, the regression line was found. Using the given data and the given regression output answer the following questions.

State    Num    Sales
1          630      15.5
2           370     7.5
3           616     13.9
4           700     18.7
5           430      8.2
6           568     13.2
7           1200    23.0
8           2976    87.3

a. What is the equation of the regression line?
b. Interpret the slope in the words of the problem.
c. Find r2 and interpret its meaning in the words of the problem.
d. Find the error for predicting the sales of a state with 1200 stores.
e. Use the regression line to predict the sales for a state with 100 stores

8. A pharmaceutical company is investigating the relationship between advertising expenditures and the sales of some over-the-counter (OTC) drugs. The following data represents a sample of 10 common OTC drugs. Find the equation of the regression line, using Advertising dollars as the independent variable and Sales as the response variable. Interpret the slope of the line in the words of the problem. Find r2 and interpret it in the words of the problem. Use the line to predict the Sales if Advertising dollars = $50 million. Note that AD = Advertising dollars in millions and S = Sales in millions $.

AD  S
22  64
25  74
29  82
35  90
38  100
42  120
46  120
52  142
65  180
88  230

Reference no: EM131036376

Questions Cloud

Union army after the battle of gettysburg : Why did President Lincoln want Grant commanding the Union army after the Battle of Gettysburg?
Determine the angular acceleration of the cylinder : Determine the angular acceleration of the cylinder and the minimum coefficient μs of friction for which the cylinder will not slip.
Developments in the mexican revolution : Discuss developments in the Mexican Revolution of 1910 to 1920. What various forces were contesting for control and what real changes took place as a result of that conflict?
Evaluate your result for ? = 30° : Neglect friction and the mass of the small end roller and find the initial acceleration of A. Evaluate your result for θ = 30°
Aptitude test on random sample : The scores on an aptitude test required for entry into a certain job position have a mean of 500 and a standard deviation of 120. If a random sample of 36 applicants has a mean of 546, is there evidence that their mean score is different from the ..
Statement for a few reasons : In Frances Schaeffer's book How Should We Then Live, Schaeffer makes a statement that says "Rome fell because it had no sufficient inward base." (Schaeffer, 1976) I agree with this statement for a few reasons. The first is because Rome was always ..
Determine the acceleration of the center o : The cord wrapped securely around the inner cylinder is fastened to point A.
Prime minister of japan and military leader : Who was the Prime minister of Japan and military leader during WWII, later executed for war crimes?
What is the plot of road of wigan pier : What is the plot of road of Wigan pier? And how does it apply to real life? Can Orwell reflect to our society?

Reviews

Write a Review

Basic Statistics Questions & Answers

  Statistics-probability assignment

MATH1550H: Assignment:  Question:  A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..

  What is the least number

MATH1550H: Assignment:  Question:     what is the least number of applicants that should be interviewed so as to have at least 50% chance of finding one such secretary?

  Determine the value of k

MATH1550H: Assignment:  Question:     Experience shows that X, the number of customers entering a post office during any period of time t, is a random variable the probability mass function of which is of the form

  What is the probability

MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?

  Binomial distributions

MATH1550H: Assignment:  Questions:  Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.

  Caselet on mcdonald’s vs. burger king - waiting time

Caselet on McDonald’s vs. Burger King - Waiting time

  Generate descriptive statistics

Generate descriptive statistics. Create a stem-and-leaf plot of the data and box plot of the data.

  Sampling variability and standard error

Problems on Sampling Variability and Standard Error and Confidence Intervals

  Estimate the population mean

Estimate the population mean

  Conduct a marketing experiment

Conduct a marketing experiment in which students are to taste one of two different brands of soft drink

  Find out the probability

Find out the probability

  Linear programming models

LINEAR PROGRAMMING MODELS

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd