Question
In: Statistics and Probability
Question 3: A sample of size 30 students is to be drawn from a population consisting...
Question 3:
A sample of size 30 students is to be drawn from a population
consisting of 300 students belonging to two colleges A and B. the
mean and standard deviations of their marks are given below:
Strata. | Total student
| mean | sd.
College A |
200.
| 30 |
10
College B. | 100
| 60 |
40
Total
| 300
| 90 |
50
Q1)How would you draw the sample using proportional allocation
techniques? Hence, obtain the variance of the estimate of the
population mean and compare its efficiency with simple random
sampling without replacement (SRSWOR).
Q2) Variance of the estimate of the population mean for simple
random sampling without replacement (SRSWOR).
Q3) Variance of the estimate of the population mean for
proportional allocation
Q4) 95% confidence interval of the population mean for proportional
allocation.
Solutions
orchestra answered 1 year agoRelated Solutions
A sample of size 30 students is to be drawn from a population consisting of 300...
A sample of size 30 students is to be drawn from a population
consisting of 300 students belonging to two colleges A and B. the
mean and standard deviations of their marks are given below:
Strata
Total number of students Ni
Mean
Standard deviation σi
College A
200
30
10
College B
100
60
40
Total
300
90
50
How would you draw the sample using proportional allocation
techniques? Hence, obtain the variance of the estimate of the
population mean...
Suppose that a sample of size 3 is drawn from a population consisting of the six...
Suppose that a sample of size 3 is drawn from a population
consisting of the six values 4, 8, 5, 3, 8, and 4, and that the
proportion of values that are greater than 4 is recorded. Find the
sampling distribution of this statistic by listing all possible
such samples of size 3. Find the mean and variance of the sampling
distribution.
A sample of size 82 will be drawn from a population with mean 24 and standard...
A sample of size 82 will be drawn from a population with mean 24
and standard deviation 9. Would it be unusual if the sample mean
was greater than 27? Why or Why not?
A sample of size 42 will be drawn from a population with mean 52 and standard...
A sample of size 42 will be drawn from a population with mean 52
and standard deviation 11.
(a) Is it appropriate to use the normal distribution to find
probabilities for x(bar)?
(b) If appropriate find the probability that x(bar) will be between
53 and 54. Round the answer to at least four decimal places.
(c) If appropriate find the 46th percentile of x(bar). Round the
answer to at least two decimal places.
A sample of size 75 will be drawn from a population with mean 35 and standard...
A sample of size 75 will be drawn from a population with mean 35
and standard deviation 10.Use the Cumulative Normal Distribution
Table if needed.
1) Find the probability that mean=x will be greater than 32.
Round the final answer to at least four decimal places.
2) Find the 65th percentile of mean=x. Round the answer to at
least two decimal places.
A sample of size 47 will be drawn from a population with mean 19 and standard...
A sample of size 47 will be drawn from a population with mean 19
and standard deviation 14. Find the probability that will be
greater than 22.
A sample of size 47 will be drawn from a population with mean 19 and standard...
A sample of size 47 will be drawn from a population with mean 19
and standard deviation 14. Find the probability that will be
greater than 22.
A sample of size 34 will be drawn from a population with mean 44 and standard...
A sample of size 34 will be drawn from a population with mean 44
and standard deviation 9.
(a) Is it appropriate to use the normal distribution to find
probabilities for x?
(b) If appropriate find the probability that x will be between 45
and 46. Round the answer to at least four decimal places.
(c) If appropriate find the 38th percentile of mean=x Round the
answer to at least two decimal places.
A sample of size 24 will be drawn from a population with mean 106 and standard...
A sample of size 24 will be drawn from a population with mean
106 and standard deviation 34
(a) Is it appropriate to use the normal distribution to find
probabilities for x?
(b) If appropriate find the probability that x will be less than
94.
(c) If appropriate find the 95th percentile of x
.
A sample of size 23 will be drawn from a population with mean 136 and standard...
A sample of size
23
will be drawn from a population with mean
136
and standard deviation
24
.
(a) Is it appropriate to use the normal distribution to find
probabilities for
x
?
(b) If appropriate find the probability that
x
will be less than
118
.
(c) If appropriate find the
80th
percentile of
x
.
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