**Sargodha University MA Economics Paper-IV Statistics for Economists Past Papers 2017**

Here you can download Past Papers of Paper-IV Statistics for Economists, MA Economics Part One, 1st & 2nd Annual Examination, 2017 University of Sargodha.

**Statistics for Economists UOS Past Papers 2017**

**M.A. Economics Part – I**

**Paper-IV(Statistics for Economics) 1 ^{st} Annual Exam.2017**

**Time: 3 Hours Marks:100**

**Note: Objective part is compulsory. Attempt any four questions from subjective Part.**

**Objective Part**

**Q.1: Write short answers of the following in two lines each.**

- Statistics
- Primary
- Frequency Distribution
- Mode
- Variance
- Index Number
- Index
- Random Variable
- Regression
- Coefficient of Determination
- Type I error

**Subjective Part**

Q.2:(a) Given the distribution of grade, find the Median, Harmonic Mean and Geometric Mean.

Grade | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |

Frequency |
8 | 87 | 190 | 304 | 211 | 85 | 20 |

b. A distribution consists of three components with components with frequencies 3,4 and 5 and having mean 2,2.5 and 10. Find the mean of the combined distribution

**Q3:** (a) The breaking strength of 20 test pieces of a certain alloy is given under: 95, 103,97,130,96,73,78,95,89,68,82,79,69,83, 108, 94, 87, 93, 117, 67. Calculate the average breaking strength of the alloy and the standard deviation. Calculate the percentage of observations lying writing the limits: mean __+__S; mean __+__ 2S; mean __+__ 3S, where S stands for the standard deviation.

**Q.4:** (a) The heights of six randomly selected sailors are in inches: 62, 64,67,68,70 and 71, and those of ten randomly selected soldiers are 62, 63, 65, 66, 69, 70, 71, 72, and 73. Discuss in the light of these data that soldiers are on the average taller than sailors. Use α = 0.05.

**b.** A standardized test in mathematics was given to 50 girls and 75 boys. The girls made and average score of 76 while the boys made an average score of 82. Assuming that the standard deviation for boys and girls was the same and was known to be 6, find a 95% confidence interval for the difference between their mean scores.

**Q.5:** (a) A bag contains 4 red and 6 black balls. A sample of 4 balls is selected from the bag without replacement. Let x be the number of red balls. Find the probability distribution for X.

b. Given the data below, test the hypothesis that the means of the three populations are equal. Let α = 0.05

Sample 1 | Sample 2 | Sample 3 |

40 | 70 | 45 |

50 | 65 | 38 |

60 | 66 | 60 |

65 | 50 | 42 |

**Q.6:** (a) Take all possible distinct samples of size two which can be drawn from a population comprising of members, 1, 3, 5, 7 and 9 without replacement. Construct sampling distribution of mean. Calculate the mean and standard deviation of this sampling distribution.

b. Let X have a binomial distribution with n = 4 and p=1/3. Find P(X=1), P(X=3/2), P(X=3), P(X=6) and P(X__<__2).

**Q.7:** (a) A study was made by a retail merchant to determine the relation between weekly advertising expenditures and sales. The following data were recorded:

Advertising |
40 |
20 |
25 |
20 |
30 |
50 |
40 |
20 |
50 |
40 |
25 |
50 |

Sales |
385 |
400 |
395 |
365 |
475 |
440 |
490 |
420 |
560 |
525 |
480 |
510 |

Find the equation of the regression line to predict weekly sales from advertising expenditure.

b. The following table given the production of cotton cloth for Pakistan from 1954 to 1963.

Year |
1954 |
1955 |
1956 |
1957 |
1958 |
1959 |
1960 |
1961 |
1962 |
1963 |

Production |
282 |
389 |
438 |
470 |
511 |
555 |
564 |
630 |
662 |
681 |

Find out index number by taking average of 1958, 1959, 1960 as base period.

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