Sppu Solved Question Papers Mcq Unit 5 1636c

University Old Question papers SPPU DEC 2013 a). Draw a histogram for the following data Wages in 0-10 10-20 ’00 Rs No. of 2 4 Workers Also find mode from the graph

20-30

30-40

40-50

50-60

11

15

25

18

OR b) i). A die is thrown 120 times and frequencies for various faces are as follows. Face No 1 2 Frequency 10 15 Given – Chi square calculated -11.40 Chi square at 0.05 ( 5 d.f)=11.070 Comment on Whether the die was fair

3 25

4 25

5 18

6 27

[5] Marks

Solution To test that the given die is fair or not Step 1 Ho : The die is fair / The die is unbiased Step 2 Ha : The die is not fair / The die is biased Step 3 -Level of Significance α =0.5 Step 4 : Data Collected Face No Frequency

1 10

2 15

3 25

4 25

5 18

6 27

Step 5 : Test statistics Computed is: 11.40 Step 6: It is given that tabulated value or critical value at 5% level of Significance at 5 (6-1) degrees of freedom is 11.07

Step 7 Decision rule: If calculated value of chi square is less than the critical value it means that is in the acceptance region. It implies that null hypothesis is accepted If calculated value of chi square is greater than the critical value it falls in the rejection region. It implies that null hypothesis is rejected and alternative hypothesis is accepted. In this case calculated chi square value is 11.4 which is greater than 11.07. It falls in the rejection region. Hence we reject null hypothesis and accept alternative hypothesis. Step 8 Inference of the experiment is that Die is not fair / Die is biased at 5% level of Significance.

b). For a sample of 400 students are found to have a mean height of 171.38cms. Can it be reasonably regarded as a sample from a large population with mean height 171.17 cms and standard deviation 3.30 cms. Given Z =1.27 (calculated) < 1.96 (tabulated) Solution To test whether the sample drawn can be regarded from the population of mean height 171.17cms and Standard deviation 3.30 cms Step 1 Ho : µ=171.17 Step 2 Ha : : µ ≠ 171.17 Step 3 -Level of Significance α =0.5 Step 4 : Data Collected for 400 students and found

X = 171.38

Step 5 : Test statistics Computed is: 1.27 Step 6: It is given that tabulated value or critical value at 5% level of Significance is 1.96

Step 7 Decision rule: If calculated Z value is less than the critical value it means that is in the acceptance region. It implies that null hypothesis is accepted If calculated Z value is greater than the critical value it falls in the rejection region. It implies that null hypothesis is rejected and alternative hypothesis is accepted.

In this case calculated Z is 1.27 which is less than critical value 1.96. It falls in the acceptance region. Hence we accept null hypothesis and reject alternative hypothesis. Step 8 The sample drawn can be regarded from the population of mean height 171.17cms with standard deviation 3.30 cms at 5% level of significance.

May 2014 a).Let the national income of a country for the years 2000-01 and 2001-02 at current prices be Rs 80650, 90010 & 90530 crores of rupees respectively and per capita income for these years be 1050,1056 and 1067 rupees. The corresponding figures of national income and per capita income at 1999-2000 prices for the above years were 80650, 80820 and 80850 crores of rupees and 1050,1051,1048 respectively. Present the data in the table. Summary of National Income and Percapita Income of a country for the period 19992002 Particulars

National Income

Percapita Income

Current prices

1999-2000 Prices 80850 80820 80650

90530 90010 80650

2001-2002 2000-2001 1999-2000

Current prices 1067 1056 1050

1999-2000 prices 1048 1051 1050

OR b).Consider the following marks obtained by 20 students in a business statistics test 64

89

63

61

78

87

74

72

54

88

62

81

78

73

63

56

83

86

83

93

Construct a stem and leaf diagram for these marks to assess class performance & Describe ths shape of these data. Solution Arrange the data in the ascending order. 54 78

56 78

61 81

Stem 5 6 7 8 9

62 83

63 83

Leaf Node 4 ,6 1,2,3,3.4 2,3,4,8,8 1,3,3,6,7,8,9 3 Total

63 86

64 87

72 88

73 89

74 93

Total 2 5 5 7 1 20

DEC 2014 Draw a histogram for the following data Salary in 30-40 (’00 Rs) No of 20 Employees

40-50

50-60

60-70

70-80

80-90

90-100

30

60

75

115

100

60

Also find the mode from the Graph.

Answer Mode is 77 b). i). The demand for a particular spare part in factory was found to vary from day to day. In a sample study the following information was obtained. [05] Day Mon No of parts 1124 demanded

Tues 1125

Wed 1110

Thurs 1120

Fri 1126

Sat 1115

Test the hypothesis that the number of parts demanded does not depend on the day of the week. Given chi square calculated =0.179. Chi square at 0.05 ( 5 d.f) =11.07 Comment on whether hypothesis is true or false with justification

Solution To test whether the demand of the particular spare part depends on the day of the week. Step 1 Ho : The demand of the particular spare part is uniformly distributed Step 2 Ha : The demand of the particular spare part is not uniformly distributed Step 3 -Level of Significance α =0.5 Step 4 : Data Collected Day Mon No of parts 1124 demanded

Tues 1125

Wed 1110

Thurs 1120

Fri 1126

Sat 1115

Step 5 : Test statistics Computed is: 0.179 Step 6: It is given that tabulated value or critical value at 5% level of Significance at 5 (6-1) degrees of freedom is 11.07 Step 7 Decision rule: If calculated value of chi square is less than the critical value it means that is in the acceptance region. It implies that null hypothesis is accepted If calculated value of chi square is greater than the critical value it falls in the rejection region. It implies that null hypothesis is rejected and alternative hypothesis is accepted. In this case calculated chi square is 0.179 which is less than the critical value 11.07. It falls in the acceptance region. Hence we accept null hypothesis and reject alternative hypothesis. Step 8 Inference of the experiment is that the demand of the spare part is uniformly distributed at 5% level of significance.

ii).Explain in detail the structure of the research report.

May 2015 a).Draw a histogram for the following data Profit in 10-20 (’00 Rs) No of 10 Companies

20-30

30-40

40-50

50-60

60-70

14

24

21

19

14

Also find the mode from the Graph. OR

b). i). The demand for a particular spare part in factory was found to vary from day to day. In a sample study the following information was obtained. [05] Day Mon No of parts 1124 demanded

Tues 1125

Wed 1110

Thurs 1120

Fri 1126

Sat 1115

Test the hypothesis that the number of parts demanded does not depend on the day of the week. Given chi square calculated =0.179. Chi square at 0.05 ( 5 d.f) =11.07 Comment on whether hypothesis is true or false with justification ii).Explain in detail the structure of the research report. DEC 2015 a). The monthly profit ( in Rs) of 100 shops are distributed are as follows. Draw a histogram for the following data Profit per 0-100 100-200 200-300 shop No of 12 18 27 shops Determine the mode of the distribution graphically.

300-400

400-500

500-600

20

17

06

OR b) i). Explain the characteristics of Good Research Report ] ii). Explain the structure of Research Report

May 2016

[5

[ 5]

a). The monthly profit ( in Rs) of 100 shops are distributed are as follows. Draw a histogram for the following data Profit per 0-100 100-200 200-300 shop No of 12 18 27 shops Determine the mode of the distribution graphically.

300-400

400-500

500-600

20

17

06

OR b) i). An automatic machine is designed to fill tins with 2Kg of oil with a standard deviation 0.1 Kg. A sample of 100 tins was examined and the average weight was found to be 1.94 Kg. Can we say that the machine is working properly. Given z=0.6 (calculated) at 5% level of Significance. Table value / critical value is 1.96 at 5% level of significance. [5] Solution To test whether the machine is working properly Step 1 Ho : µ= 2 Kg Step 2 Ha : : µ ≠ 2 Kg Step 3 -Level of Significance α =0.5 Step 4 : Data Collected for 100 students and found

X = 1.94 Kg

Step 5 : Test statistics Computed is: 1.06 Step 6: It is given that tabulated value or critical value at 5% level of Significance is 1.96 Step 7 Decision rule: If calculated Z value is less than the critical value it means that is in the acceptance region. It implies that null hypothesis is accepted If calculated Z value is greater than the critical value it falls in the rejection region. It implies that null hypothesis is rejected and alternative hypothesis is accepted.

In this case calculated Z is 1.06 which is less than critical value 1.96. It falls in the acceptance region. Hence we accept null hypothesis and reject alternative hypothesis. Step 8 The sample drawn can be regarded from the population of mean weight of 2 Kg. It infers that the machine is working properly at 5% level of significance.

ii). Explain the characteristics of good Research Report

Dec 2016

New Pattern 2016

[5]

Dec 2016

Solution To test whether there is association between the internet access and the purchasing intention of cellular phone Step 1

Ho : There is no association between the internet access and the purchasing intention of cellular phone Step 2 Ha : There is an association between the internet access and the purchasing intention of cellular phone Step 3 -Level of Significance α =0.5 Step 4 : Data Collected

Step 5 : Test statistics Computed is: 72 Step 6: It is given that tabulated value or critical value at 5% level of Significance at 1 degree of freedom is 3.84 Step 7 Decision rule: If calculated value of chi square is less than the critical value it means that is in the acceptance region. It implies that null hypothesis is accepted If calculated value of chi square is greater than the critical value it falls in the rejection region. It implies that null hypothesis is rejected and alternative hypothesis is accepted. In this case calculated chi square is 72 which is greater than the critical value 3.84. It falls in the rejection region. Hence we reject null hypothesis and accept alternative hypothesis. Step 8 Inference of the experiment is that there is association between the internet access and the purchasing intention of cellular phones at 5% level of significance.

Multiple Choice Questions 1) Which analysis is related with descriptive analysis? a) Univariate Analysis b) Bivariate Analysis c) Multivariate Analysis d) All of the above 2) Involves the orderly and systematic representation of numerical data in a form designed to elucidate the problem under consideration a) Coding b) Classification c) Editing d) Tabulation 3) Which frequency expresses the number of items in an interval as a proportion or fraction of the total number of items in the data set? a) Relative frequency b) Percentage Frequency c) Cumulative frequency d) None of the above 4) Which steps involves in processing operations of data after collection of data? a) Coding b) Classification c) Editing d) Tabulation 5) Which is type of frequency distribution? a) Continuous or grouped frequency distribution b) Discrete or ungrouped frequency distribution c) Cumulative Frequency Distribution d) All of the above 6) One where measurements are only approximations and are expressed in class intervals ie within certain limits is a) Continuous Frequency Distribution b) Discrete Frequency Distribution c) Cumulative Frequency Distribution d) All of these Frequency Distribution 7) In which Graphical Representation, way of preparing a two-dimensional diagram is in the form of circles? a) Pie Chart b) Histogram

c) Candle Stick d) None of the above 8) In which analysis, when there is a single measurement of each of the n sample objects or where there are several measurements of each of the n observations but each variable is analysed in isolation? a) Univariate Analysis b) Bivariate Analysis c) Multivariate Analysis d) None of these 9) If a group of N observations is arranged in ascending or descending order of magnitude, then the middle value is called a) Mean b) Median c) Mode d) None of these 10) Which is the type of correlation on the basis of number of variables? a) Positive correlation b) Multiple correlation c) Linear Correlation d) Non-linear Correlation 11) Which characteristics come under Karl Pearson’s Coefficient of Correlation? a) Does not tell anything about cause-and-effect relationship b) Independent of change of origin and scale c) Varies between -1 and +1 d) All of the above 12) If one knows that the yield and rainfall are closely related then one want to know the amount of rain required to achieve a certain production. For this purpose we use analysis a) Regression Analysis b) Coefficient of Correlation c) Scatter Plots/Diagram d) None of these 13) When two attributes are present or absent together in the data and actual frequency is more than the expected frequency is called a) a).Positive Association b) b).Negative Association c) c).Independent Association d) d). None of these 14) Which is test of significance of means for small sample ? a) t- test b) z-test c) F-test d) Q-test

15)Which test is the part of the parametric test? a) Sign Test b) Run Test for Randomness c) Kruskal-Willis Test d) z-test 16) …………. Analysis is a mathematical tool which is used to describe the degree to which one variable is linearly related to each other. a) Regression b) correlation c) variance d) none of these 17) Which analysis comes under inferential analysis? a) Univariate Analysis b) Bivariate Analysis c) Multivariate Analysis d) Hypothesis Testing 18) The procedure of classifying the answers to a question into meaningful categories is called a) Coding b) Classification c) Editing d) Tabulation 19) Which of the following constitute the essential elements of coding? a) Mutually exclusive b) Single Dimension c) Code Sheet d) all of these 20) Which among the following is type of frequency? a) Relative frequency b) Percentage frequency c) Cumulative frequency d) All of the above 21) A bar chart or graph showing the frequency of occurrence of each value of the variable being analysed is called a) Bar Chart b) Histogram c) Candle stick d) None of these 22) A chart is a style of bar-chart used primary to describe price movements of a security, derivative, or currency over time is called a) Leaf and stem b) Histogram c) Candle Stick

d) Bar chart 23) A group of observations is the quotient obtained by dividing the sum of all the observations by their number, is called a) Mean b) Median c) Mode d) None of these 24) Which analysis is the simultaneous analysis of two variables? a) Univariate Analysis b) Bivariate Analysis c) Multivariate Analysis d) None of these 25) Which Statistical tool comes under Bivariate Analysis ? a) Linear Regression Analysis b) Association of Attributes c) Two-way ANOVA d) All of the above 26) The assumption of normal distribution for the variable under consideration or some assumption for a parametric test is not valid or is doubtful then we use a) Parametric Test b) Non-Parametric Test c) Both Parametric Test and Non-Parametric Test d) All of the above 27) What is abbreviation of ANOVA? a) Analysis of variance b) Analysis of variation c) Analysis of variant d) None of these 28 ). The smallest and the largest possible measurements in each class are known as class…………. (a) Boundaries (b) interval (c) limits (d) mark 29). The value exactly at the middle of a class interval is called………. (a) Mid value (b) class mark (c) limits (d) both (a) & (b) 30). The number of observations falling within a particular class interval is called its class………… a) Frequency

b) interval c) limits d) mark 31. ………… includes letters, questionnaires, tests or other tools used in collecting the data. (a) Appendix (b) glossary (c) literature cited (d) bibliography 32. A ……….is an alphabetical listing of unfamiliar with their meaning used in the thesis. (a) Appendix (b) glossary (c) literature cited (d) bibliography 33. ……….is a comprehensive listing of the works relevant to the study of the researcher. (a) Appendix (b) glossary (c) literature cited (d) bibliography 34. When a hypothesis relates to the cause and effect relationship of a phenomenon it is called………. (a) Tentative (b) descriptive (c) explanatory (d) hypothesis concerning law 35. Rejecting a true null hypothesis is committing a………….. (a) type- I error (b) type-II error (c) type- III error (d) sampling error 36. In testing of hypothesis, if the null hypothesis is rejected ………. Hypothesis is accepted (a) Alternative (b) relational (c) new (d) none of these 37.Population measurements are called ………… (a) Parameters (b) statistics (c) estimates (d) hypotheses 38.Where the sample size is less than 30 ….is used. (a) F- test (b)Z- test (c) T- test (d)U- test

39. Reporting means ……….through reports (a) Asking (b) answering (c) communicating (d) stating 40.The method helps to predict the unknown values of one variable from the known values of another variable are called ………analysis. (a) Correlation (b) regression (c) factor (d) cluster 41………. Is a measure of central tendency? (a) Mean (b) standard deviation (c) mean deviation (d) range 42.When the study is related with more than two variables, it is termed as…… (a) bivariate (b) multivariate (c) casual (d) unidimensional 43.If a table shows the relationship between two variables in a tabular form, it is called a …table (a) Frequency (b) simple (c) complex (d) contingency 44. What does it mean when you calculate a 95% confidence interval? (a) The process you used will capture the true parameter 95% of the time in the long run (b) You can be “95% confident” that your interval will include the population parameter (c) You can be “5% confident” that your interval will not include the population parameter (d) All of the above statements are true 45. What is the median of the following set of scores? 18, 6, 12, 10, 14 ? (a) 10 (b) 14 (c) 18 (d) 12 46 . The median is ______. (a) The middle point (b) The highest number (c) The average (d) Affected by extreme scores

47. The most frequently occurring number in a set of values is called the ____. (a) Mean (b) Median (c) Mode (d) Range 48. As a general rule, the _______ is the best measure of central tendency because it is more precise. (a) Mean (b) Median (c) Mode (d) Range 49. The standard deviation is: (a) The square root of the variance (b) A measure of variability (c) An approximate indicator of how numbers vary from the mean (d) All of the above 50. ……… statistics is used to describe the basic features of the data in a study. (a) (b) (c) (d)

Descriptive business inferential none of these