State whether the following statements are true or false. Give brief justification.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
b) If the odds in favour of an event A are 3 : 4, then the probability of occurrence of A
will be 4/7.
c) If the level of significance is the same, the area of the rejection region in a 2-tailed
test is less than that in a 1-tailed test.
d) There is no seasonal variation in an annual time series.
e) In a binomial distribution, if X represents the number of successes in 25 trials and the
probability of success at each trial is 0.5, then the standard deviation of X is 2.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
False. The number of samples of size 3 with replacement from a population of size 6 is not 20. When sampling with replacement, each selection is independent, and for each of the 3 selections, you have 6 choices (since you replace the item after each selection). So, the total number of possible samples is 6 * 6 * 6, which is 216, not 20.
b) If the odds in favor of an event A are 3 : 4, then the probability of occurrence of A will be 4/7.
False. The odds and probability are related but not the same. To find the probability of an event from its odds, you can use the following formula:
Probability (A) = Odds in Favor of A / (Odds in Favor of A + 1)
In this case, the odds in favor of A are 3:4, so:
Probability (A) = 3 / (3 + 4) = 3/7
Therefore, the
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The frequency distribution of marks of 230 students in a statistics paper in a class is given below:
Class Interval Frequency
10 – 20 12
20 – 30 30
30 – 40 ?
40 – 50 65
50 – 60 ?
60 – 70 25
70 – 80 18
Total 230
Given that the median value of distribution is 46, determine the missing frequencies.
25 samples of 6 items each were selected from the assembly line of a machine. On
measurement of a critical dimension, the mean X of 25 sample means was reported
as 0.81 inches and ï’ as 0.0025 inches. Compute the control limits for the X and
R charts.
Calculate the 5-yearly moving average for the following data of the profits of a
company (in Rs. Lakhs) during 1995 to 2010:
.
Does each of the following statements pertain to an estimate or an estimator? If the
statement pertains to an estimate is it an interval estimate or point estimate? If the
statement pertains to an estimator write the estimator.
i) The head of a publishing company says that the firm’s physics textbook will sell
about 9000 copies in 2012.
ii) A cencus prefers the median to the mean as a measure of central tendency for the
income distribution of families in a standard metropolitan city.
iii) A stock market analyst who appears on the television programme, estimates that
the price of a particular common stock will be between 50 and 60 at the end of
six months
The monthly income (in Rs. Lakhs) of five employees in a company are as follows:
25, 20, 30, 15, 10. (i) List all possible samples (without replacement) of size 2 (ii)
Compute the mean of all samples and set up the sampling distribution of sample
mean.
There are 40 pages in a book numbered from 1 to 40. A page is opened at random.
Find the probability that the number of that opened page is a multiple of 3 or 5.
A hospital has 25 centres located at different places in a state. Each centre has been provided with 4 paramedics. In order to estimate the average number of patients handled by a paramedic on a typical day at a centre, a sample of 5 centres was selected, using without replacement simple random sampling. The data regarding the number of patients on a typical working day for each selected centre are given below:
| Centre | m | Patients seen | |||
| 1 | 4 | 1 | 2 | 6 | 3 |
| 2 | 4 | 4 | 3 | 2 | 2 |
| 3 | 4 | 5 | 3 | 2 | 1 |
| 4 | 4 | 4 | 1 | 5 | 6 |
| 5 | 4 | 2 | 3 | 4 | 7 |