Solve your IGNOU Doubts

Question:

a) Tariff barriers are not the only instrument to restrict trade and give protection to the domestic import competing industry.

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Question:

b) Highlight the main advantages and disadvantages of TNCs operations for the host country and the investing country

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Question:

a) Explain various theories explaining emergence of TNCs in the world economy.

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Question:

b) What is political risk? Discuss the major types of political risk with examples.

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Question:

a) Define international business environment. Differentiate between micro and macro environment with examples.

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Question:

If you are told that haemoglobin (Hb) level in blood measures the iron content. The normal level in healthy people is around 15 g/dL. Most Indian women have less and some have even less than 8 g/dL. They are called anemic. Iron supplementation is given to increase this level. Suppose one supplementation increase the mean Hb level in anemics by 3.2 g/dL, after one month of use and the other by 3.6 g/dL, in an equivalence trial on 500 women each. The respective SD’s of the of the increases are 0.52 and 0.72 g/dL. The doctors determine that the supplementations can be clinically equivalent if the difference between the increases by two supplementations does not exceed 0.52 g/dL. Can these two supplementations be considered clinically equivalent at 5% level of significance?

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Question:

In usual notations you are given the following information $\delta =0.05,\, \pi_1=0.75,\, \pi_2=0.65,\, \bar{\pi}=0.7,\alpha =0.05,\, \beta =0.20$ Find the sample size. If power of the test is 95% instead of 80%, then find new sample size.

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Question:

RTPCR test is applied on 300 covid patients and 200 non-covid patients. The results of the test are shown as follows.

		Disease status
		Yes (D ⁺ )	No (D ^- )	Total
Result of RTPCR test	_T+	480	40	520
	_T-	120	360	480
	Total	600	400	1000

What are the sensitivity and specificity of the test? Also, determine the positive and negative values of the test.

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Question:

What is the basic difference between (a) cross-sectional (b) cohort and (c) case control study designs. Explain with suitable examples of each design.

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Question:

A trial is conducted in which some people with disease X were randomly allocated into twogroups. First group was advised to do some morning walk for 30 minutes and take light foodeach day and second group was given one injection and one 100 mg tablet once a day tocontrol disease X. The injection can cause loose motion in some cases and 100 mg tablethas no side effect. At the end of two months, 90% of group I and 80% of group II had
recovered from disease X.
i) What are the regimens for group I and group II in this trial?
ii) What are the efficacies in group I and group II?
iii) What are the safety issues in group I and group II in this trial?

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Question:

If p denotes proportion and q denotes odds then prove that $q=\frac{p}{1-p}.$ Find the range of q. If the odds of smokers in a study are 0.25 then find the proportion of smokers in the study. Assume that each subject of the study is either a smoker or non-smoker.

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Question:

In the natural history of a disease define: total preclinical phase, detectable pre-clinical phase and clinical phase. Suppose on 10 am on 25.01.2010 a disease A onset you biologically. Suppose test of the disease A can detect it exactly after completion of 1000 days of biologically onset. Suppose signs and symptoms develop exactly after completion of 1010 days of biologically onset. Suppose you consult doctor exactly after 1015 days of biologically onset of the disease. Suppose outcome the treatment is cure. What is duration of (i) total preclinical phase (ii) detectable pre-clinical phase (iii) clinical phase.

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Question:

$X\sim N_3\left ( \mu ,\sum \right )$ with $\mu=\begin{pmatrix} 2\\ 1 \\ 2 \end{pmatrix}$ and $\sum=\begin{pmatrix} 5 & 3&0 \\ 3 &3 & -2\\ 0 & -2 & 5 \end{pmatrix}.$ Then find the joint distribution of $X_1+2X_2,2X_1-X_2 and X_3.$

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Question:

Define the following:
(i) Covariance Matrix
(ii) Mahalanobis D2
(iii) Hotelling’s T2
(iv) Clustering
(v) Relationship between (ii) and (iii).

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Question:

Obtain the maximum likelihood estimator of the mean vector and variance-covariance matrix of the multivariate normal distribution.

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Question:

Consider the following data of 11 samples on 8 variables by Anscombe, Francis J. (1973):

$x_1$	$x_2$	$x_3$	$x_4$	$y_1$	$y_2$	$y_3$	$y_4$
10	10	10	8	8.04	9.14	7.46	6.58
8	8	8	8	6.95	8.14	6.77	5.76
13	13	13	8	7.58	8.74	12.74	7.71
9	9	9	8	8.81	8.77	7.11	8.84
11	11	11	8	8.33	9.26	7.81	8.47
14	14	14	8	9.96	8.10	8.84	7.04
6	6	6	8	7.24	6.13	6.08	5.25
4	4	4	19	4.26	3.10	5.39	12.50
12	12	12	8	10.84	9.13	8.15	5.56
7	7	7	8	4.82	7.26	6.42	7.91
5	5	5	8	5.68	4.74	5.73

If the vector $x=\begin{pmatrix} x_1\\ x_2 \\x_3 \\ x_4 \end{pmatrix}$ and $y=\begin{pmatrix} y_1\\y_2 \\ y_3 \\ y_4 \end{pmatrix}$ then obtain the sample covariance matrix between x and y

Source: Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17– 21. doi: 10.2307/2682899.

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Question:

Let $X\sim N_4\left ( \mu ,\sum \right ),$ where $\mu =\begin{pmatrix} 3\\ -2 \\1 \\ -2 \end{pmatrix}$ and $\sum=\begin{pmatrix} 4 & 0 & 0 & 0\\0 & 3 & 0 &0 \\ 0 & 0 & 2 & -2\\ 0 & 0 & -2 & 5 \end{pmatrix}.$ Check the independence of the (i) $X_2$ and $X_1$ (ii) ( $X_2$ , $X_4$ ) and ( $X_1$ , $X_3$ ) (iii) ( $X_1$ , $X_2$ ) and ( $X_3$ , $X_4$ ).

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Question:

Let X be a 3-dimensional random vector with dispersion matrix

$\sum=\begin{pmatrix} 4 &-2 & 0\\ -2 & 4 &0 \\ 0 & 0 & 2 \end{pmatrix}.$ Determine the first principal component and the proportion of the total variability that it explains.

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Question:

$X=\binom{X^{(1)}}{X_{(2)}}\sim N_4\left ( \mu ,\sum \right ),$ where $\begin{pmatrix} -4\\ \frac{1}{4} \\ 0 \end{pmatrix}$ and $\sum=\begin{pmatrix} \begin{matrix} 2&2 \\ 2& 1\end{matrix} & \begin{matrix} 3&0 \\ 2& 0\end{matrix} \\ \begin{matrix} 3&2 \\ 0& 0\end{matrix} & \begin{matrix} 2&1 \\ 1& 1\end{matrix} \end{pmatrix}.$ Find the