Question

5-1. Consider a random sample of size 36 from a normal distribution (population) with a mean of 10 and a standard deviation of 6. Which of the following statement is false?

(a) The mean of X¯ is 10. (b) The standard deviation of X¯ is 1. (c) X¯ approximately follows a normal distribution. (d) There is an incorrect statement in the alternatives above.

5-2. Let X1, . . . , X36 be a random sample from Bin(36, 0.5). Which of the following statements is false?

(a) The mean of X¯ is 18. (b) The standard deviation of X¯ is 1/3. (c) The mean of P36 i=1 Xi is 648. (d) The standard deviation of P36 i=1 Xi is 18. (e) X¯ approximately follows a normal distribution.

Answer #1

Solution :

1) mean = = 10

standard deviation = = 6

n = 36

= = 10

= / n = 6 / 36 = 1

a) False statement is -(d) There is an incorrect statement in the alternatives above.

2)

b) approximately follows a normal distribution.

a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,neab,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths placee

a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,neab,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths place

1. A sample size of 49 drawn from a population with a mean of 36
and a standard deviation of 15 for the size of an English class.
What is the probability the class will have greater than 40
a. .9693
b. .4693
c. .0808
d. .0307
2. A sample size of 49 drawn from a population with a mean of 36
and a standard deviation of 15 for the size of an English class.
What is the probability the...

what is the approximate distribution of the mean of a random sample
size 36 frim a population whose mean and standard deviation are 20
and 12 respectively? why?

A random sample of size 13 was taken from a population with a
population mean 27 and a population standard deviation 5.
Determine each of the following about the sampling distribution
of the sample mean.
Awnser A, B, C
Round your answer to at least 3 decimal places where
appropriate.
a) μx_=
b) σx_=
c) Can we conclude that the sampling distribution of
the sample mean is approximately normal? Yes or No

Which of the following is NOT true regarding the sampling
distribution of the mean (Sample mean X-bar) for a large sample
size (sample size is greater than 36)? A. It has the same mean as
the population. B. It has a smaller standard deviation than the
population standard deviation. C. Approximately it follows a normal
distribution. D. It has the same distribution as the
population.

A random sample of size n1 = 25, taken from a normal
population with a standard deviation σ1 = 5.2, has a
sample mean = 85. A second random sample of size n2 =
36, taken from a different normal population with a standard
deviation σ2 = 3.4, has a sample mean = 83. Test the
claim that both means are equal at a 5% significance level. Find
P-value.

5. You have a random sample of 1,627 for the random
variable Xi. The sample mean is 26.2 and the sample standard
deviation is 39.1. Define µ as the population mean for Xi. Assume
that µ = 20. (LO4) a. Sketch the distribution of X ̅. b.
Graphically illustrate the p-value associated with X̅= 26.2.

Suppose X1,...,X20 are a random sample of size 20 from
N(100,100) population. What are the distributions of the following
quantities?
(a) sample mean: X(bar) = (1/20) (X1 + . . . + X20);
(b) a scaled sample variance: (19/100)S^2, where S^2 = (1/19)
*SIGMA from i=1 to 20* (Xi - X(bar))^2;
(c) standardized mean: (X(bar) - 100) / (10/sqrt(20));
(d) studentized mean: (X(bar) - 100) / (S/sqrt(20))

15. Random samples of size 81 are taken from an infinite
population whose mean and standard deviation are 200 and 18,
respectively. The distribution of the population is unknown. The
mean and the standard error of the mean are (assuming infinite
population)
a. 200 and 18
b. 81 and 18
c. 9 and 2
d. 200 and 2
16. A population has a mean of 300 and a standard deviation of
18. A sample of 144 observations will be taken....

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