DRM 02
Hypothesis Testing
Assignment - I
Assignment Code: 2017DRM02B1 Last Date of Submission: 15th November 2017
Maximum Marks: 100
Attempt all the questions.
SECTION – A (25 marks for each question)
1. a) Explain why do we carry out Hypothesis testing.
b) Discuss the different types of Errors Type I and Type II while conducting hypothesis testing.
c) Discuss the following approaches we adopt for either Rejection or otherwise of the Null Hypothesis:
(i) Critical value approach
(ii) Confidence Interval approach
(iii) p-value approach
2. A certain brand of wheat flour is offered for sale in the market in gunny bags, each weighing 25Kg nominal with a standard deviation of 0.25Kg. A buyer decides to check the average bag weight on a sample of 64 bags. He makes up his mind to accept the average weight if the sample weight is 24.9kg or more and 25.10kg or less. What is the probability that the average weight of each bag is accepted as much as claimed?
SECTION – B
Case Study (50 marks)
A cardiologist was interested in understanding whether there is any difference in the cholesterol levels of his patients who come with cardiac ailments. He felt that since non vegetarians eat considerable protein than fat their level of cholesterol would be somewhat less than those of vegetarians (since they tend to consume more of fat and oil in their food intake.) In order to test his hypothesis, the cardiologist chose to conduct an experiment. He randomly selected from his patients 12 non –vegetarians and 12 vegetarians for his study with the consent of the patient. He took their blood samples and sent to his laboratory to test their cholesterol levels and found the following data:
Non veg patients 232 245 183 275 180 195 212 232 240 280 292 196
Veg Patients 245 256 232 275 300 297 320 280 275 344 289 300
The doctor from his basic knowledge of statistics knew that before he could carry out the relevant hypothesis test, he should look at the descriptive statistics and obtained the following results.
Descriptives
Patient Statistic Std. Error
Cholesterol levels Non Veg Mean 230.16 11.04936
Median 232.00
Variance 1465.0
Std. Deviation 38.27
Skewness .261 .637
Kurtosis -1.158 1.232
Veg Mean 284.41 9.03986
Median 284.50
Variance 980.629
Std. Deviation 31.31
Skewness .129 .637
Kurtosis .060 1.232
The doctor also knew that there are several other assumptions before he can proceed with understanding his research question. Based on your knowledge you are required to help him with the following:
(i) Write down the null and alternative hypothesis for the above research problem.
(ii) Test the two samples have equal variances. Use 5% level of significance.
(iii) Use the appropriate hypothesis test to check whether indeed non-vegetarians have lower cholesterol levels than do vegetarians. Use 5% level of significance.
(iv) Verify your assumptions based on the output given above.
DRM 02
Hypothesis Testing
Assignment - II
Assignment Code: 2017DRM02B2 Last Date of Submission: 15th November 2017
Maximum Marks: 100
Attempt all the questions.
SECTION-A (25 marks for each question)
1. In hypothesis testing, we use both Z test and ‘t’ statistic for testing the single mean test. Explain when we would use a Z test and when we would use a ‘t’ statistic. Explain the other assumptions associated with each of these tests.
2. A random sample of size 10 from a normal population produced the following values:
63 72 68 74 77 65 61 71 73 69
Test the hypothesis that population variance is 32.
SECTION-B (50 marks)
In 2003, Mumbai based Care Hygiene Co. (Care Hygiene), a well-known company dealing in healthcare products, recorded sales of Rs.665 crores and a net income of Rs. 45.6 crores. ‘Nutravit’, a chocolate flavored health drink, was one of its flagship products. But of late, Nutravit has been facing stiff competition from a number of other chocolate-based beverages that had flooded the market. Its market share had significantly come down. Care Hygiene decided it was high time it took some efforts to tackle competition and regain market share. The company decided to market a new variant of Nutravit, with an improved formulation and in a new flavor.
By mid-2003, Care Hygiene was ready with its new variant – a powdered mix which when mixed with milk gave a nutritious as well as tasty vanilla cum chocolate flavoured drink. He selected Mumbai and Nagpur as the test cities because there were significant similarities in the consumption patterns of its health drink ‘Nutravit’ in these two cities. In Mumbai, Care continued to market its established health beverage, while in Nagpur it replaced it with the new Vanilla cum chocolate flavor.
In each city, a sample of 200 households were selected and interviewed over a six-month period. Based on each household’s reported consumption of beverages, Care’s marketing manager chartered the results showing the different household consumption rates in Mumbai and Nagpur.
Consumption Rate Nagpur
(Vanilla cum chocolate) Mumbai
(Chocolate)
Number % households Number % households
Heavy 34 17 28 14
Moderate 52 26 44 22
Light 50 25 42 21
Non-User 64 32 86 43
Total 200 100 200 100
In Mumbai, where the chocolate flavored was marketed, 114 households reported using the beverage. In Nagpur, where the new variant was test marketed, 136 households reported using the beverage mix.
1. Care’s marketing manager wondered if the difference in usage rates (57% in Mumbai and 68% in Nagpur) could be attributed to the new vanilla formulation or if the difference had merely resulted by chance due to sampling.
2. Since the new formulation was an improved one with a new flavor, it was more expensive. The management decided to proceed with it only if there was sufficient evidence that the new variant would yield better results. While test marketing the new variant, Care’s marketing manager had decided that if it achieved a 75% usage rate among target households, he would recommend the launching of the product. What should he do? Based on the sample of 200 households, the new variant had achieved a usage rate of 68%. Should he recommend to the management for or against launching of the new product?
Hypothesis Testing
Assignment - I
Assignment Code: 2017DRM02B1 Last Date of Submission: 15th November 2017
Maximum Marks: 100
Attempt all the questions.
SECTION – A (25 marks for each question)
1. a) Explain why do we carry out Hypothesis testing.
b) Discuss the different types of Errors Type I and Type II while conducting hypothesis testing.
c) Discuss the following approaches we adopt for either Rejection or otherwise of the Null Hypothesis:
(i) Critical value approach
(ii) Confidence Interval approach
(iii) p-value approach
2. A certain brand of wheat flour is offered for sale in the market in gunny bags, each weighing 25Kg nominal with a standard deviation of 0.25Kg. A buyer decides to check the average bag weight on a sample of 64 bags. He makes up his mind to accept the average weight if the sample weight is 24.9kg or more and 25.10kg or less. What is the probability that the average weight of each bag is accepted as much as claimed?
SECTION – B
Case Study (50 marks)
A cardiologist was interested in understanding whether there is any difference in the cholesterol levels of his patients who come with cardiac ailments. He felt that since non vegetarians eat considerable protein than fat their level of cholesterol would be somewhat less than those of vegetarians (since they tend to consume more of fat and oil in their food intake.) In order to test his hypothesis, the cardiologist chose to conduct an experiment. He randomly selected from his patients 12 non –vegetarians and 12 vegetarians for his study with the consent of the patient. He took their blood samples and sent to his laboratory to test their cholesterol levels and found the following data:
Non veg patients 232 245 183 275 180 195 212 232 240 280 292 196
Veg Patients 245 256 232 275 300 297 320 280 275 344 289 300
The doctor from his basic knowledge of statistics knew that before he could carry out the relevant hypothesis test, he should look at the descriptive statistics and obtained the following results.
Descriptives
Patient Statistic Std. Error
Cholesterol levels Non Veg Mean 230.16 11.04936
Median 232.00
Variance 1465.0
Std. Deviation 38.27
Skewness .261 .637
Kurtosis -1.158 1.232
Veg Mean 284.41 9.03986
Median 284.50
Variance 980.629
Std. Deviation 31.31
Skewness .129 .637
Kurtosis .060 1.232
The doctor also knew that there are several other assumptions before he can proceed with understanding his research question. Based on your knowledge you are required to help him with the following:
(i) Write down the null and alternative hypothesis for the above research problem.
(ii) Test the two samples have equal variances. Use 5% level of significance.
(iii) Use the appropriate hypothesis test to check whether indeed non-vegetarians have lower cholesterol levels than do vegetarians. Use 5% level of significance.
(iv) Verify your assumptions based on the output given above.
DRM 02
Hypothesis Testing
Assignment - II
Assignment Code: 2017DRM02B2 Last Date of Submission: 15th November 2017
Maximum Marks: 100
Attempt all the questions.
SECTION-A (25 marks for each question)
1. In hypothesis testing, we use both Z test and ‘t’ statistic for testing the single mean test. Explain when we would use a Z test and when we would use a ‘t’ statistic. Explain the other assumptions associated with each of these tests.
2. A random sample of size 10 from a normal population produced the following values:
63 72 68 74 77 65 61 71 73 69
Test the hypothesis that population variance is 32.
SECTION-B (50 marks)
In 2003, Mumbai based Care Hygiene Co. (Care Hygiene), a well-known company dealing in healthcare products, recorded sales of Rs.665 crores and a net income of Rs. 45.6 crores. ‘Nutravit’, a chocolate flavored health drink, was one of its flagship products. But of late, Nutravit has been facing stiff competition from a number of other chocolate-based beverages that had flooded the market. Its market share had significantly come down. Care Hygiene decided it was high time it took some efforts to tackle competition and regain market share. The company decided to market a new variant of Nutravit, with an improved formulation and in a new flavor.
By mid-2003, Care Hygiene was ready with its new variant – a powdered mix which when mixed with milk gave a nutritious as well as tasty vanilla cum chocolate flavoured drink. He selected Mumbai and Nagpur as the test cities because there were significant similarities in the consumption patterns of its health drink ‘Nutravit’ in these two cities. In Mumbai, Care continued to market its established health beverage, while in Nagpur it replaced it with the new Vanilla cum chocolate flavor.
In each city, a sample of 200 households were selected and interviewed over a six-month period. Based on each household’s reported consumption of beverages, Care’s marketing manager chartered the results showing the different household consumption rates in Mumbai and Nagpur.
Consumption Rate Nagpur
(Vanilla cum chocolate) Mumbai
(Chocolate)
Number % households Number % households
Heavy 34 17 28 14
Moderate 52 26 44 22
Light 50 25 42 21
Non-User 64 32 86 43
Total 200 100 200 100
In Mumbai, where the chocolate flavored was marketed, 114 households reported using the beverage. In Nagpur, where the new variant was test marketed, 136 households reported using the beverage mix.
1. Care’s marketing manager wondered if the difference in usage rates (57% in Mumbai and 68% in Nagpur) could be attributed to the new vanilla formulation or if the difference had merely resulted by chance due to sampling.
2. Since the new formulation was an improved one with a new flavor, it was more expensive. The management decided to proceed with it only if there was sufficient evidence that the new variant would yield better results. While test marketing the new variant, Care’s marketing manager had decided that if it achieved a 75% usage rate among target households, he would recommend the launching of the product. What should he do? Based on the sample of 200 households, the new variant had achieved a usage rate of 68%. Should he recommend to the management for or against launching of the new product?
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