STATISTICAL INFERENCE & QUANTITATIVE RESEARCH SPRING-2022
ASSIGNMENT # 03
Q.1.
An advertising company wants to estimate with 98% confidence interval, the number of
times a website is hit during an hour. It is determined that 𝜎 = 26. How large a sample should
the company take, if it wishes that the margin of error should not exceed 10?
Q.2.
If we take a sample from an infinite population, what will happen to the standard error of the
mean when the sample size is increased from 60 to 240?
Q.3.
A sample of 16 Ten-Years old girls had a mean weight of 71.54 pounds and a standard
deviation of 12 pounds.
(a) What assumption is necessary for the validity of the confidence interval constructed?
(b) What is the estimated standard error?
(c) Construct a 95% confidence interval for the population mean.
Q4.
A college has 500 students. A survey was carried out on 22 students chosen at random to
find out the
average number of siblings. The following data is obtained: 2, 1, 3, 2, 0, 1, 2,
4, 0, 1, 1, 0, 1, 3, 2, 0, 1, 2, 2, 1, 0, 1 ; Find the 90% confidence interval for the mean
number of sibling of the college students.
Q.5.
In measuring reaction time, a psychologist estimated that standard deviation is 0.05 seconds.
How large a sample of measurements must be taken in order to 95% confident that the error
in his estimate of mean reaction time will not exceeds 0.01 seconds.
Q.6.
A random sample of 20 boys was taken to estimate the 98% confidence interval for the mean
weight of boys aged between 14 to 15 years. The 98% confidence interval was found to be
45.5 < 𝜇 < 51.3. Find the sample mean and sample variance.
Q.7.
The following results are obtained in an IQ - TEST taken by 50 boys and 60 girls:
BOYS
GIRLS
∑X1 = 4910
∑X2 = 5676
∑X12 = 483515
∑X22 = 537481
Construct the 95% Confidence Interval for the difference between the IQ-TEST of Boys and
Girls.
Q.8.
The following data were obtained from an experiment designed to estimate the reduction in
Blood Pressures as a result of following a salt free diet for two weeks:
BEFORE
93
106
87
92
102
95
88
110
AFTER
92
102
89
92
101
96
88
105
Assuming that the Blood Pressures of the population are normally distributed, find the 98%
confidence interval for the mean reduction in Blood Pressures.
BEST OF LUCK
From the desk of ASIF SUMEER
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