In: Statistics and Probability

use
the population {3,4,6} and assume that samples of size 2 are
randomly selected, with replacement. a) for the population, find
the proportion of odd numbers. b) construct a table for sampling
distribution of the sample proportion of odd numbers. c) find the
mean of sampling distribution of the sample proportion of odd
numbers. d) is the sample proportion and unbiased estmator or.
biased estimator of the population? Why?

**Answer:**

Given that,

Use the population {3,4,6} and assume that samples of size 2 are randomly selected, with replacement.

**(a).**

**For the population, find the proportion of odd
numbers:**

From the given problem the population is {3,4,6}.

The proportion of odd numbers is,

In the data set {3,4,6} is odd number count is
**1.**

Therefore, the proportion of odd numbers is
**1/3**.

**(b).**

**Construct a table for the sampling distribution of the
sample proportion of odd numbers:**

The table representing the sampling distribution of the sample proportion of odd numbers is,

The data set is {3,4,6}

Sample |
Proportion (P) |

(3,4) | 1/2 |

(3,6) | 1/2 |

(4,6) | 0 |

**(c).**

**Find the mean of the sampling distribution of the sample
proportion of odd numbers:**

The mean of the sampling proportions,

Thus, the required mean is **1/3.**

**(d).**

**Is the sample proportion and unbiased estimator [or] a
biased estimator of the population:**

From the previous results,

**=P**

Thus, the sample proportion is an **unbiased
estimator** of the population proportion.

Use the population {3,4,6} and assume that samples of size 2 are
randomly selected, with replacement.
?) For the population, find the proportion of odd numbers
?) Construct a table for the sampling distribution of the sample
proportions of odd numbers.
?) Find the mean of the sampling distribution of the sample
proportion of odd numbers.
?) Is the sample proportion an unbiased estimator or a biased
estimator of the population proportion? why?

Suppose samples of size 100 are drawn randomly from a population
of size 1000 and the population has a mean of 20 and a standard
deviation of 5. What is the probability of observing a sample mean
equal to or greater than 21?

7. Use the population of {1, 3, 7}. Assume that the random
samples of size n = 2 Construct a sampling distribution of the
sample mean. After identifying the 9 different possible samples
(with replacement), find the mean of each sample, then construct a
table representing the sample the sampling distribution of the
sample mean. In the table, combine values of the sample mean that
are the same. (Hint: condense the table similar to examples
presented in class.)
a. Sample...

Assume that a population of size 5 specifies that all possible
samples of size "3" are extracted without repetition.
Values:
2,500.00
2,650.00
2,790.00
3,125.00
3,200.00
1) Show that the expected value of the standard sampling error
is greater than the standard deviation of the population.
2) Calculate the confidence interval of the sample means with
a significance level of 80% and indicate which samples are not
representative and develop an analysis.
3) Select the non-representative samples and calculate the
mean...

Assume that a population of size 5 specifies that all possible
samples of size "3" are extracted without repetition.
Values:
2,500.00
2,650.00
2,790.00
3,125.00
3,200.00
1. Show that the expected value of the standard sampling error
is greater than the standard deviation of the universe.
2. Select a sample and calculate the mean of the universe mean
with a confidence level of 84% and develop an analysis.

Assume that the samples are independent and that they have been
randomly selected. Construct a 90% confidence interval for the
difference between population proportions p1-p2. Round to three
decimal places. x1=12, n1=45 and x2=21, n2=51
A.
-0.301 <p1-p2< 0.011
B.
0.453 <p1−p2 < 0.079
C.
0.109 <p1−p2< 0.425
D.
0.081 <p1−p2< 0.453

Assume a population of 1,2 and 12. assume the sample size of
size n = 2 are randomly selected with replacement from the
population. listed below are the nine different sample. complete
parts a through d below
1,1 1,2 1,12, 2,1 2,2 2,12 12,1 12,2 12,12
a) find the value of the population standard deviation
b) find the standard deviation of each of the nine samples the
summarize the sampling distribution of the standard deviation in
the format of a...

Random samples of size n = 90 were selected from a
binomial population with p = 0.8. Use the normal
distribution to approximate the following probability. (Round your
answer to four decimal places.)
P(p̂ > 0.78) =

Random samples of size n = 60 were selected from a
binomial population with p = 0.2. Use the normal
distribution to approximate the following probabilities. (Round
your answers to four decimal places.)
(a)
P(p̂ ≤ 0.22) =
(b)
P(0.18 ≤ p̂ ≤ 0.22) =

Two samples, one of size 13 and the second of size 18, are
selected to test the difference between two population means and
σ is unknown.
Which distribution should be used for this test?
What is the critical value for a 10% level of significance for a
right tail test?

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- You work for SneauxCeauxne, the Cajun-inspired crushed-ice dessert company. You’ve collected data on monthly sales (S,...
- Taxation Questions Q1: Anna converted cryptocurrency into $27,200 Australian dollars in October 2019. To complete the...
- Discussion: The Strategy of Cultivating Interdependence All of life is an opportunity to think, relate, and...
- People in the aerospace industry believe the cost of a space project is a function of...
- O’Brien Company manufactures and sells one product. The following information pertains to each of the company’s...
- The S&P 500 stock price closed at $98, $103, $107, $102, $111 over five successive weeks....
- Sal Amato operates a residential landscaping business in an affluent suburb of St. Louis. In an...

ADVERTISEMENT