Unit 5 Business Statistics and Research Methods PYQ’s 26th Nov 2021 Shift 1

The correct answer is – Less than 8%

Key Points

Average Annual Growth Rate

• The average annual growth rate (AAGR) reports the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis.
• It doesn’t take compounding into account.
• The average annual growth rate helps determine long-term trends.
• It applies to almost any kind of financial measure including growth rates of profits, revenue, cash flow, expenses, etc. to provide the investors with an idea about the direction wherein the company is headed.

Important Points

• From the first year to second year, the growth rate was from 5% to 12% which means 7% growth.
• Then from second to third year the growth rate was from 12% to 7%. The growth rate declined by 5%.
• Hence, it can be said that the average annual increase over this period would be less than 8%.

The correct answer is – PE = .6745(1 − r²)√n

Key Points

Probable Error:

• Probable Error is basically the correlation coefficient that is fully responsible for the value of the coefficients and its accuracy
• It also helps in measuring the coefficient’s dependability.
• A population’s correlation coefficient is often based on the sample and the knowledge of the correlation coefficient.
• Therefore, determining or obtaining the correlation coefficient of any population is simple when using probable error.

Formula : PE = .6745(1 − r²)√n

Here, r = correlation coefficient of ‘n’ pairs of observations for any random sample and N = Total number of observations.

The correct answer is – “No change in Pearson’s coefficient of skewness value”

Key Points

Pearson’s coefficient of skewness:

• This method is most frequently used for measuring skewness.
• The value of this coefficient would be zero in a symmetrical distribution.
• If mean is greater than mode, coefficient of skewness would be positive otherwise negative.
• The value of the Karl Pearson’s coefficient of skewness usually lies between +/-1 for moderately skewed distribution.

Hence, the correct answer No change in Pearson’s coefficient of skewness value.

The correct answer is – The coefficients are revised by byx = 0.24 and bxy = 4.0

Key Points

Bivariate Data:

• Bivariate data deals with two variables that can change and are compared to find relationships.
• If one variable is influencing another variable, then we will have bivariate data that has an independent and a dependent variable. This is because one variable depends on the other for change.
• When a bivariate data in a particular equation is multiplied or divided by certain values, the value of the coefficients is affected in regression.
• The coefficients will get revised.

Important Points

A certain bivariate data byx and bxy have been calculated, which are equal to 2.4 and 0.4, respectively.

Let x series be ‘u’ and y series be ‘v’.

Hence,

u = 5 × x

v = y2

Suppose new coefficients values be ‘c’ and ‘d’.

Hence,

u = xc

v = yd

b_xy = b_uv × cd

b_yx = b_vu × dc

u = x1/5

Hence, c = 15

v = y2

Hence, d = 2

b_xy = 0.4(given)

b_yx = 2.4(given)

New coefficients values will be:

b_uv = 0.4 × 21/5

b_uv = 4

b_vu = 2.4 × (1/5)2

b_vu = 0.24

Hence, If the value of the x series are all multiplied by 5 and all values of y series are divided by 2 the coefficients are revised by byx = 0.24 and bxy = 4.0

The correct answer is – B and C only

Key Points

The values in one of the series in a bivariate data set are multiplied by a constant K, Standard deviation and covariance between the variables would change because standard deviation and covariance are dependent on scale, that is why the value of standard deviation and covariance will change after multiplying by a constant K and correlation is independent of scale that’s why it will not change.

Important Points

Additional Information

Change of Origin: It means some value is added or subtracted to the value of the origin. For example : If the value of Standard Deviation is 10 and as the value of standard deviation is not dependent of origin so if any value is added to the variables the value of 10 will remain constant.

Change of Scale: It means some value is multiplied or divided to the value. For Example; If the value of Standard Deviation is 10 and as the value of standard deviation is dependent on scale so if any value is multiplied or divided to the variables, it will also change.

The correct answer is – B, A, E, C, D, F

Key Points

Using statistics, hypothesis testing is a formal process for examining our theories about the world. Scientists most frequently employ it to examine particular hypotheses that result from theories.

Important Points

Process of Hypothesis Testing are as follows:

• Setup Null and Alternate Hypothesis
• Select the Significance Level
• Select Test Statistics
• Establish the Decision Rule
• Performance Computations
• Draw Conclusions

The correct answer is – A – lV, B – ll, C – l, D – lll

Key Points

The correct match is given below:

Important Points

Dispersion :The process of becoming distributed or spread is called dispersion. The probability that numerical data may differ from an average value is known as statistical dispersion. In other words, dispersion aids in understanding how the data are distributed.

Karl Pearson’s measures of skewness : Karl Pearson developed two methods of calculating skewness based on relationship between averages which are as follows:

(a) Pearson’s Coefficient of Skewness using the Mode

Sk = Mean – Mode / Standard Deviation

(b) Pearson’s Coefficient of Skewness using the Median

Sk = 3(Mean – Median) / Standard Deviation

Bowley’s Measure of Skewness: Bowley also given the formula to calculate value of skewness using the relationship between quartile and median, formula for the same is:

[(Q3+Q1)] – 2median] / Q3- Q1

Kelly’s Measure of Skewness: Kelly also given the formula to calculate skewness using the percentile and Decile, formula is

Kelly’s Percentile coefficient of Sk =[(P90+P10)- 2 Median] /P90 – P10

Kelly’s Decile coefficient of Sk = [(D9 + D1) – 2median] / D9- D1

The correct answer is – A, B and D only

Key Points

The correct answer is A, B and D only because option C ,i.e., the critical value of Z for one tailed test with α = 0.05 is 1.96 is incorrect as the critical value of Z for one tailed test with α = 0.05 is 1.645 not 1.96.

Important Points

Upper Tailed Test

Lower Tailed Test

Two -Tailed Test