The standard error of the sample mean is given by the formula $SE = \frac{\sigma}{\sqrt{n}}$. Option C matches this definition assuming standard notation.
Q2mcq1 mark
Rejecting H0, when it is true is called :
a.
sampling error
b.
type I error
Correct Answer
c.
standard error
d.
type II error
Step-by-Step AI Explanation
Verified Method
In hypothesis testing, rejecting the null hypothesis $H_0$ when it is actually true is defined as a Type I error. Sampling error refers to the natural variation between samples, standard error is the measure of the dispersion of a statistic, and Type II error occurs when we fail to reject a false null hypothesis.
Q3mcq1 mark
The degrees of freedom of the chi-square test statistic for the contingency of order 5Γ4 :
a.
12
Correct Answer
b.
18
c.
25
d.
17
Step-by-Step AI Explanation
Verified Method
The degrees of freedom for a chi-square test in a contingency table of size $r \times c$ is calculated as $(r-1)(c-1)$. For a $5 \times 4$ contingency table, degrees of freedom $= (5-1)(4-1) = 4 \times 3 = 12$.
Q4mcq1 mark
In two-way classification TSS=
a.
SST1SSBβSSE
b.
SST1SSB1SSE
Correct Answer
c.
SST1SSB
d.
SSTβSSB1SSE
Step-by-Step AI Explanation
Verified Method
In two-way ANOVA classification, the Total Sum of Squares (TSS) is the sum of the sum of squares between rows (SSR), columns (SSC), and error (SSE). Therefore, $TSS = SSR + SSC + SSE$.
Q5mcq1 mark
If Ξ£D2=0, then rank correlation is :
a.
0.5
b.
0
c.
β1
d.
1
Correct Answer
Step-by-Step AI Explanation
Verified Method
Spearman's rank correlation coefficient is given by $r_R = 1 - \frac{6 \Sigma D^2}{n(n^2-1)}$. If $\Sigma D^2 = 0$, then $r_R = 1 - \frac{6(0)}{n(n^2-1)} = 1 - 0 = 1$.
Q6mcq1 mark
If bXY=0.7 and βaβ=8 then the regression equation of X on Y is :
a.
Y=0.718X
b.
Y=810.7X
c.
X=0.718Y
Correct Answer
d.
X=810.7Y
Step-by-Step AI Explanation
Verified Method
The regression equation of $X$ on $Y$ is given by $X = a + b_{XY}Y$. Given $b_{XY} = 0.7$ and $a = 8$, substituting these into the formula yields $X = 8 + 0.7Y$. Option C represents this form.
Q7mcq1 mark
If the two lines of regression are perpendicular to each other, then rXY =
a.
β1
b.
0
Correct Answer
c.
2
d.
11
Step-by-Step AI Explanation
Verified Method
The two lines of regression are perpendicular if the angle between them is $90^\circ$. This occurs when the correlation coefficient $r = 0$, meaning there is no linear relationship between the variables.
Q8mcq1 mark
In simple aggregate method, the aggregate price of all items in the given year is expressed as percentage of the same in the :
a.
Quarterly
b.
Current year
c.
Half-yearly
d.
Base year
Correct Answer
Step-by-Step AI Explanation
Verified Method
In the simple aggregate method for index numbers, the price index is calculated as $\frac{\Sigma P_1}{\Sigma P_0} \times 100$, where $\Sigma P_1$ is the aggregate of current year prices and $\Sigma P_0$ is the aggregate of base year prices. Thus, it is expressed as a percentage of the base year.
Q9mcq1 mark
Data of annual turnover of a company over a period of ten years can be represented by :
a.
a parameter
b.
a time series
Correct Answer
c.
a statistic
d.
index numbers
Step-by-Step AI Explanation
Verified Method
A time series is a set of observations recorded at specific time intervals (e.g., annually over ten years). This matches the definition of tracking turnover over time. Parameters, statistics, and index numbers are descriptive measures or summaries but do not represent the sequence of data over time itself.
Q10mcq1 mark
Business forecast is made on the basis of :
a.
tax regulations
b.
future data
c.
Government policies
d.
past data
Correct Answer
Step-by-Step AI Explanation
Verified Method
Business forecasting relies on analyzing trends and patterns observed in the past to predict future outcomes. While government policies and taxes impact the business environment, the foundational basis for the forecast models is historical or past data.
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Medication: 10 12 9 15 13
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Calculate (1) Laspeyreβs Index (2) Paascheβs Index (3) Marshall-Edgeworth Index and (4) Fisher Ideal Index for the following data taking 2014 as base year.
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Number of deaths recorded in various age groups in two areas and the population size in each age group are given in the following table. Find the crude death rate and age specific death rate of Area I and Area II.
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