Mid Term Inferential Business 2018 doc

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FACULTY OF BUSINESS Mid-Exam, 2017 - 2018

Inferential Statistics to Business - Thursday morning Exam Duration: 2 hrs

Instructor: Dr. Padilla Rosa

Student name: ______________________________________________________________________________ ID: ____________

INSTRUCTIONS

Answer ALL questions, show ALL work to be graded. No credit will be given for answer only responses. If you use software SPSS to answer a question, please put the steps you took to get to the answer and interpret all the necessary output for each question.

Write the answers for questions number 3 part (a) on this paper, and write the rest of the questions inside the answer booklet.

1. The scores of a random sample of 8 students on a physics test are as follows: 60, 62, 67, 69, 70, 72, 75, and 78.

a. (2 marks) Test to see if the sample mean is significantly different from 65 at the .05 level. Report the t and p values. b. (2 marks) Find the confidence interval of 97% of the population for the score of the physics test and interpret result. c. (2 mark) Find and interpret mean and standard deviation for the problem

d. (2 marks) Test the assumption about Normality

2. (7 marks) The college president asks the statistics teacher to estimate the average age of the students at their college. How large a sample is necessary? The statistics teacher would like to be 99% confident that the estimate should be accurate within 0.5 year. From a previous study, the standard deviation of the ages is known to be 2.5 years.

3. A (hypothetical) experiment is conducted on the effect of alcohol on perceptual motor ability. Ten subjects are each tested twice, once after having two drinks and once after having two glasses of water. The two tests were on two different days to give the alcohol a chance to wear off. Half of the subjects were given alcohol first and half were given water first. The scores of the 10 subjects are shown below. The first number for each subject is their performance in the "water" condition. Higher scores reflect better performance.

a. (8 marks) Test to see if alcohol had a significant effect. Report the t and p values. (Independent t samples). b. (5 marks) Test the assumption about that the population variances are equal.

c. (2 marks) Interpret mean and standard deviation for the problem.

FACULTY OF BUSINESS

Mid-Exam, 2017 - 2018

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Inferential Statistics to Business -

Thursday morning

Exam Duration: 2 hrs

Student name: ______________________________________________________________________________ ID: ____________

INSTRUCTIONS

1 (4 marks) Describe the difference between a probability sample and non probability sample.

2 (7 marks) Suppose we have 1200 primary teachers. In a previous investigation, we found that 20 percent plan to retire in the next 5 years; we want to estimate how many teachers will retire in the near future. How many elementary teachers do we have to collect if we have 90 percent confidence and the maximum margin of error of 10 percent?

3 A researcher investigating the effectiveness of different forms of advertising randomly selects ten subjects to take part in an experiment to determine if reaction time to a visible stimulus (visual) is different from reaction time to an audible stimulus. The null hypothesis in this case is that there is no difference between reaction time of visual and auditory stimuli. The data are set out in the following table:

a. (8 marks) Test the appropriate hypothesis with all the steps you learned in our course, especially put emphasis on the interpretation according to the variables of the problem.

b. (3 marks) Test the assumption about Normality

c. (2 marks) Find and interpret mean and standard deviation for the problem

4 The following data represent a sample of the assets (in millions of Rwandan franks) of 12 credit unions in Rwanda.

12.2 16.5 4.9 2.8 1.2 2.7 13.1 9.3 5.6 8.9 3.5 13.4

a. (3 marks) Find the 90% confidence interval of the mean and interpret result b. (2 marks) Find and interpret mean and standard deviation for the problem c. (1 mark) Test the assumption about Normality

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Student name: ______________________________________________________________________________ ID: ____________

INSTRUCTIONS

Write the answers inside the answers booklet, and write the answer for the question number 3 part (a) on this paper.

1. (5 marks) Describe the difference between an Inferential Statistics and Descriptive Statistics.

2. The following data represent a sample of the assets (in millions of Rwandan franks) of 12 credit unions in Rwanda.

12.2 16.5 4.9 2.8 1.2 2.7 13.1 9.3 5.6 8.9 3.5 13.4

a. (4 marks) Find the 90% confidence interval of the mean

b. (2 marks) Interpret mean and standard deviation for the problem c. (2 marks) Test the assumption about Normality

3. Who do you think has a better sense of humor-women or men?

Researchers asked 8 men and 8 women in their study to categorize 30 cartoons as either “funny” or “funny”. Each participant received a score that represents her or his percentage of cartoons found to be “funny”. Below are fictional data for 16 people; these fictional data have approximately the same means as were reported in the original study (Azim, Mobbs, Jo, Menon and Reiss, 2005).

Percentage of cartoons labeled as “funny”.

a. (8 marks) How can we conduct a hypothesis for this scenario, using a two-tailed test and a significant level of 0.05 b. (2 marks) Test the assumption about that the population variances are equal.

c. (2 marks) Interpret mean and standard deviation for the problem.

4. (5 marks) Suppose a survey researcher studying expenditures on a set of school supplies to buy. He wants to have a 95% confidence level and a range of error of less than $2.00. If the estimated of standard deviation is $19.00. Calculate the sample size.

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Student name: ______________________________________________________________________________ ID: ____________ INSTRUCTIONS

1. A Social Work Department wishing to validate an empathy scale gives the measure to intending Social Workers and compare with other group that is Non social workers. The following table shows the scores of the two groups on the empathy measure.

Do the scores indicate that intending Social Workers have higher empathy scores than non-Social Workers?

a. (8 marks) Test the appropriate hypothesis with all the steps that you learn in our course, especial put emphasis in interpretation according the variables of the problem.

b. (2 marks) Test the assumption about that the population variances are equal. c. (2 marks) Interpret mean and standard deviation for the problem.

2. The following raw scores represent the final examination grade for Geography in National University of Rwanda: Student Raw score inGeography

Sylvie 5

Clementine 18

Alloys 17

Assinath 15

Moustapha 14

Fliny 10

Alphonsine 12

a. (3 marks) Psychometricians like to use confidence intervals because they more accurately represent the fact that the observed scores are only estimated with respect to the student's actual score. For this reason build and interpret a 90% confidence interval for the raw score in Geography.

b. (3 marks) Conduct the appropriate statistical test of your hypothesis, using a .05 statistical significance. The teacher of the course believe that the score of Geography is less than before (µ < 10), and assuming that the score follow normal distribution.

c. (2 marks) Test the assumption about that the population distribution are normal. 3. (5 marks) What information is necessary to calculate a confidence interval?

4. (5 marks) How many cities’ growing seasons would have to be sampled in order to estimate the true mean growing season with 95% confidence within 7 days? (Use the standard deviation of 54.2 days.)

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Mid-Exam, 2017 - 2018

Inferential Statistics to Business – Thursday morning Exam Duration: 2 hrs

Student name: ______________________________________________________________________________ ID: ____________

INSTRUCTIONS

1. We want to estimate the average income of the credit cooperatives in the Western Province of Rwanda. A random sample of 11 credit unions is shown. The information is in thousands Rwandans francs.

84 14 31 72 26 49 25 31 18 72 24

a. (4 marks) Find the confidence interval of 90% of the population for the income of the credit cooperatives in the Western Province.

2. (5 marks) What is necessary to determine the sample size?

3. (5 marks) An insurance company is trying to estimate the average number of sick days that full-time food service workers use per year. A pilot study found the standard deviation to be 4 days. How large a sample must be selected if the company wants to be 95% confident of getting an interval that contains the true mean with a maximum error of 1 day?

4. Ten cars were equipped with radial tires and driven over a test course. Then the same 10 cars (with the same drivers) were equipped with regular belted tires and driven over the same course. After each run, the cars’ gas economy (in km/l) was measured.

Car

Gas eco. 1 2 3 4 5 6 7 8 9 10

Y1 (radial) 4.2 4.7 6.6 7 6.7 4.5 5.7 6 7.4 4.9

Y2 (belted) 4.1 4.9 6.2 6.9 6.8 4.4 5.7 5.8 6.9 4.7

a. (8 marks) Is there evidence that radial tires produce better fuel economy? (Assume normality of data, and use  = .05.) Ho:

Ha: α= Statistics= P_value or Sig.=

Making a decision and interpreting the results:

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Inferential Statistics to Business - Evening Exam Duration: 2 hrs

Student name: ______________________________________________________________________________ ID: ____________

INSTRUCTIONS

1. (7 marks) A health care professional wishes to estimate the birth weights of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within 3 ounces of the sample mean? The standard deviation of the birth weights is known to be 8 ounces.

2. Find the 94% confidence interval for the mean number of local jobs for top corporations in southern province. A sample of 13 selected corporations is shown.

12 7 11 23 5 9 12 10 2 6 6 13 10

a. (4 marks) Find the confidence interval of 94% of the population for the income of the credit cooperatives in the southern Province.

3. Ten sets of identical twins were enrolled in a study to measure the effect of home environment on certain social attitudes. One twin in each set was randomly assigned to a minority environment or a home environment. The twin assigned to the minority environment went to live with an African American family for a period of 1 year. At the end of the year, an attitudinal survey was administered. The data along with some descriptive statistics follow. Let alpha = 0.05

Table 1. Raw data for attitude versus environment study

ID 1 2 3 4 5 6 7 8 9 10

Home 65 67 75 77 69 65 73 78 70 72

Minor 83 75 72 76 78 80 72 81 70 78

a. (8 marks) Test the hypothesis that living in the minority environment leads to higher scores on the attitudinal survey. Ho:

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Student name: ______________________________________________________________________________ ID: ____________

INSTRUCTIONS

1. The data represent a sample of the number of home fires started by candles for the past several years. (Data are from the National Fire Protection Association.)

5460 5900 6090 6310 7160 8440 9930

a. (4 marks) Find the 99% confidence interval for the mean number of home fires started by candles each year. b. (2 marks) Interpret mean and standard deviation for the problem

c. (2 marks) Test the assumption about Normality

2. (7 marks) The federal report in the previous exercise also stated that 88% of children under age 18 were covered by health insurance in 2000. How large a sample is needed to estimate the true proportion of covered children with 90% confidence with a confidence interval 0.05 wide (5% error)?

Source: Washington Observer-Reporter

3. A (hypothetical) experiment is conducted on the effect of alcohol on perceptual motor ability. Ten subjects are each tested twice, once after having two drinks and once after having two glasses of water. The two tests were on two different days to give the alcohol a chance to wear off. Half of the subjects were given alcohol first and half were given water first. The scores of the 10 subjects are shown below. The first number for each subject is their performance in the "water" condition. Higher scores reflect better performance.

a. (8 marks) Test to see if alcohol had a significant effect. Report the t and p values.. b. (3 marks) Test the assumption about that the population variances are equal. c. (4 marks) Interpret mean and standard deviation for the problem.

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1. A sample of 12 funeral homes in Toledo, Ohio, found these costs for cremation (in dollars). 1320 1052 1090 1285 1570 995 1150 1585 820 1195 1160 590. Source: Toledo Blade. a. (4 marks) Find the 95% confidence interval for the population mean.

2. (7 marks) A university dean wishes to estimate the average number of hours that freshmen study each week. The standard deviation from a previous study is 2.6 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 0.5 hour?

3. A researcher investigating the effectiveness of different forms of advertising randomly selects ten subjects to take part in an experiment to determine if reaction time to a visible stimulus (visual) is different from reaction time to an audible stimulus. The null hypothesis in this case is that there is no difference between reaction time of visual and auditory stimuli. The data are set out in the following table:

Subjects

Reaction time to visual stimulus

(m.secs)

Reaction time to auditory stimulus

(m.secs)

1 259 260

2 275 257

3 304 300

4 285 287

5 288 290

6 314 312

7 291 285

8 304 300

9 246 245

a. (8 marks) Test the appropriate hypothesis with all the steps you learned in our course, especially put emphasis on the interpretation according to the variables of the problem.

b. (4 marks) Test the assumption about Normality

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FACULTY OF BUSINESS Mid-Exam, 2017 - 2018 Inferential Statistics to Business - Friday

Exam Duration: 2 hrs Instructor: Dr. Padilla Rosa

1. A Social Work Department wishing to validate an empathy scale gives the measure to intending Social Workers and compare with other group that is Non social workers. The following table shows the scores of the two groups on the empathy measure. Do the scores indicate that intending Social Workers have higher empathy scores than non-Social Workers?

a. (8 marks) Test the appropriate hypothesis with all the steps that you learn in our course, especial put emphasis in interpretation according the variables of the problem.

b. (3 marks) Test the assumption about that the population variances are equal. c. (4 marks) Interpret mean and standard deviation for the problem.

2. A random sample of stock prices per share (in dollars) is shown.

26.69 13.88 28.37 12 75.37 7.5 47.5 43 53.81 13.62 45.12

a. (4 marks) Find the 90% confidence interval for the prices. Assume the variable is normally distributed. b. (2 marks) Interpret mean and standard deviation for the problem

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1. (7 marks) A survey by Brides magazine found that 8 out of 10 brides are planning to take the surname of their new husband. How large a sample is needed to estimate the true proportion within 3% with 90% confidence?

Source: Time magazine

2. The sugar content (in grams) for a random sample of 4-ounce containers of applesauce is shown. 18.6 19.5 20.2 20.4 19.3 21 20.3 19.6 20.7 18.9 22.1 19.7

a. (4 marks) Find the 99% confidence interval for the population variance and standard deviation. Assume the variable is normally distributed.

3. Who do you think has a better sense of humor-women or men?

Researchers asked 6 men and 8 women in their study to categorize 30 cartoons as either “funny” or “funny”. Each participant received a score that represents her or his percentage of cartoons found to be “funny”. Below are fictional data for 14 people; these fictional data have approximately the same means as were reported in the original study (Azim, Mobbs, Jo, Menon and Reiss, 2005).

Percentage of cartoons labeled as “funny”.

a. (8 marks) How can we conduct a hypothesis for this scenario, using a two-tailed test and a significant level of 0.05 b. (4 marks) Test the assumption about that the population variances are equal.

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1. The following raw scores represent the final examination grade for Inferential Statistics to Business: Student Claudine Shadrack Odette Ajio Bonaventure Pierre Judith Heredion Patrick

Score in

Inferential 78 68 47 55 34 20 62 82 90

a. (2 marks) Psychometricians like to use confidence intervals because they more accurately represent the fact that the observed scores are only estimated with respect to the student's actual score. For this reason build and interpret a 99% confidence interval for the raw score in Inferential Statistics.

b. (2 marks) Conduct the appropriate statistical test of your hypothesis, using a statistical significance α= .05. The course teacher believe that the Inferential Statistics score is better than before (µ > 50).

d. (2 marks) Interpret mean and standard deviation for the problem.

2. (7 marks) The Ministry of Economy places each of its employees on one of three salary scales, A, B, and C. The number of employees on each scale is listed below: How many employees from each scale should be included in a sample of size, with a 90% confidence interval and a maximum sampling error of 2 %.

A 100

B 375

C 543

3. Eight sets of identical twins were enrolled in a study to measure the effect of home environment on certain social attitudes. One twin in each set was randomly assigned to a minority environment or a home environment. The twin assigned to the minority environment went to live with an African American family for a period of 1 year. At the end of the year, an attitudinal survey was administered. The data along with some descriptive statistics follow. Let alpha = 0.05

Raw data for attitude versus environment study

ID 1 2 3 4 5 6 7 8

Home 65 67 75 77 69 65 73 78

Minor 83 75 72 76 78 80 72 81

a. (8 marks) Test the hypothesis that living in the minority environment leads to higher scores on the attitudinal survey. Ho: