ASSIGNMENT No. 1
(Units 1–5)
Q.1 a) In a normal distribution 31% of the item are under 45 and 8% are over 64. Find the mean and
standard deviation of the distribution.
b) If X ~ N (π, σ2) and P (X < 35) = 0.20 and P (35 < X < 45) = 0.65. Find μ
and σ.
c) A finite population consists of the numbers 2, 3, 4, 5, 6 and 8. Find the proportion of even
numbers in all possible random samples of size n = 2 that can be drawn with replacement
from this population. Assuming the 36 possible samples equally likely make the sampling
distribution of sample proportions, find the mean and variance of this distribution. Verify that
i) E (P) = π ii) Var (P) =
n
)1(
Where P and π are sample and population proportions respectively.
Q.2 a) Define the terms: statistical inference, null and alternative hypothesis, level of significance,
test statistic, type-I and type-II error,
b) A sample of 400 male students is found to have a mean height of 67.47 inches. Can it be
regarded as a simple random sample from a large population with mean height 67.39 inches
with standard deviation of 1.3 inches?
Q.3 a) A random sample of 25 hens from a normal population showed that the average laying is 272
eggs per year with a variance of 625 eggs. The company claimed that the average laying is at
least 285 eggs per year. Test the claim of the company at 5% level of significance.
b) The sex distribution of 98 births reported in a newspaper was 52 boys and 46 girls. Is this
consistent with an equal sex division in the population? Use 5% level of significance.
Q.4 a) An examination was taken to two classes of 40 and 50 students respectively. In the first class,
mean grade was 74 with a standard deviation of 8, while in the second class the mean grade
was 78 with a standard deviation of 7. Is there a significant difference between the mean
grades at 1% level of significance?
b) The I.Q.’s of 16 students from one area of a city showed a mean of 107 with a standard
deviation of 10, while the I.Q.’s of 14 students from another area of the city showed a mean
of 115 with a standard deviation of 8. Is there a significant difference between the I.Q.’s of
the two groups at (i) 0.01 and (ii) 0.05 level of significance?
Q.5 To verify whether a course in statistics improved performance a similar test was given to 12
participants both before and after the course. The original grades recorded in alphabetical order of
the participants were 44, 40, 61, 52, 32, 44, 70, 41, 67, 72, 53 and 72. After the course, the grades
were in the same order, 53, 38, 69, 57, 46, 39, 73, 48, 73, 74, 60 and 78.
a) Was the course useful, as measured by performance on the test? Considered these 12
participants as a sample from a population.
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