CSS 2022 Statistics Past Paper

Paper details

Examination

CSS

Year

2022

Subject

Statistics

Paper

Single Paper

Subject type

Optional

Mode

Subjective

Questions recorded from this paper

These 7 question wordings are transcribed from CSS Vista’s structured Statistics past-paper record for CSS 2022.

1. Q2 · Descriptive and Inferential Statistics(a) What can you say of the skewness in each of the following cases? (09) i) The median is 60 while the two quartiles are 40 and 80. ii) Mean = 140 and Mode = 140. The first three moments about 16 are respectively -0.35, 2.09 and -1.93. (b) Discuss the various measures or quantities by which the characteristics of frequency (06) distributions are measured and compared. (c) Differentiate between descriptive and inferential statistics. (05) (20)
2. Q4 · Basic Probability(a) A company has 800 employees. Twenty percent of the employees have college degrees (10) but half of these people are in non-management positions. Thirty percent of the non- degree people are in management positions. i) How many managers does the company have? ii) What is the conditional probability of being a college graduate is a manager? iii) Find the probability of randomly selecting someone who is either a college graduate or a manager. (b) A soft drink machine is regulated so that it discharges an average of 200 milliliters per cup. If the (10) (20) amount of drink is normally distributed with a standard deviation equal to 15 millimeters. i) What is the probability that a cup contains between 191 and 209 milliliters? ii) How many cups will likely overflow if 230 milliliters cups are used for the next 1000 drinks? iii) Below what value do we get the smallest 25% of the drinks?
3. Q3 · Part – II (50 marks)The following data give information on the ages (in years) and the number of (20) breakdowns during the past month for a sample of seven machines at a large company. Age 12 7 2 8 13 9 4 Number of breakdowns 10 5 1 4 12 7 2 i) Taking age as independent variable and the number of breakdowns as a dependent variable what is your hypothesis about the sign of B in the regression line. ii) Compute SSxx, SSyy, and SSxy. iii) Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part i. iv) Calculate r and r2 and explain what they mean. v) Predict the number of breakdowns for age equal to 10 years. vi) Compute the standard deviation of errors. vii) Construct a 90% confidence interval for B. viii) Test the hypothesis H 0 :   0 against   0 .
4. Q5 · Sampling Distribution of Mean(a) A study of time spent on housework found that men who are employed spend an average of 8.2 (10) hours per week doing housework (Americans’ Use of Time Project, University of Maryland, American Demographics, November 1998). Assume that the amount of time spend on housework per week by all employed men in the United States is normally distributed with a mean of 8.2 hours and a standard deviation of 2.1 hours. i) What is the probability that a randomly selected employed man spends 9 or more hours per week on housework? ii) What is the probability that a randomly selected employed man spends 7 hours or less on housework per week? (b) A population consists of N = 6 numbers 0, 1, 5, 6, 8 and 11. Draw all possible samples of size n (10) (20) = 3, without replacement, from the population and find the sample means. Construct the sampling distribution of sample means and verify that: )  2  N n  x)   and Var( X )    n  N 1 
5. Q7 · difference between two Means(a) Given the following ANOVA for a RCB design (12) S.V d.f. SS MS Blocks 8 2.1074 treatments 3 2.1006 Error 24 2.6249 i) Complete the analysis; fill in the mean squares ii) Compute the standard error for a treatment and for the difference between two treatment means. iii) Treatment means are 1.464, 1.195, 1.325 and 1.662. What mean or means do you suspect might represent different population by applying LSD test. (b) Define the relative efficiency. How would you calculate the relative efficiency of LS design (08) (20) relative to RCB design with rows as blocks?
6. Q6 · Difference between two means and Difference between two proportions(a) A candidate for mayor in a large city believes that he appeals more of the women voters than the (10) men voters. He hires the services of a poll-taking organization, and they find that 62 out of 100 women interviewed support the candidate, and 69 out of 150 men support him. Calculate 99% confidence interval for the difference between two proportions. (b) Explain the six steps of Tests of Hypothesis. (10) (20)
7. Q8 · Index Numbers(a) Construct the following weighted aggregative price index numbers for 1990 and 1991 from the (12) given data: i) Laspeyres’ index ii) Paasche’s index iii) Fisher’s “Ideal” index Prices (Rs. per 40 kg) Quantities (tons) Commodity 1986 (base) 1990 1991 1986 1990 1991 (b) Describe the importance of vital statistics. Also state its uses and limitations. (08) (20) ttps:///

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