位置8的问题 Random samples of size 100 are taken from a process (an infinite population) whose population proportion is 0.2. The mean and standard deviation of the distribution of sample proportions are _____. 20 and 0.040.2 and 0.040.2 and 0.2None of the alternative answers is correct.Single choice
A
20 and 0.04
B
0.2 and 0.04
C
0.2 and 0.2
D
None of the alternative answers is correct.

Question

位置8的问题 Random samples of size 100 are taken from a process (an infinite population) whose population proportion is 0.2. The mean and standard deviation of the distribution of sample proportions are _____. 20 and 0.040.2 and 0.040.2 and 0.2None of the alternative answers is correct.Single choice

A

20 and 0.04

B

0.2 and 0.04

C

0.2 and 0.2

D

None of the alternative answers is correct.

BlackTom AI · Accepted Answer

The question asks for the mean and standard deviation of the distribution of sample proportions when drawing samples of size 100 from an infinite population with population proportion p = 0.2.

First, recall that for a binomial-based sampling model, the sampling distribution of the sample proportion p̂ has a mean equal to the population proportion p. So the mean should be p = 0.2.

Second, the standard deviation (standard error) of p̂ is sqrt[p(1 − p) / n] for a sample size n. Here, p = 0.2 and n = 100, so the calculation is sqrt[0.2 × 0.8 / 100] = sqrt[0.16 / 100] = sqrt[0.0016] = 0.04.

Thus, the pair (mean, standard deviation) is (0.2, 0.04).

Now evaluate the options:
- Option "20 and 0.04": This is incorrect because the mean cannot be 20 for a proportion; proportions range between 0 and 1.
- Option "0.2 and 0.04": This matches the correct mean and standard deviation as derived above.
- Option "0.2 and 0.2": Here the standard deviation is miscomputed; 0.2 would imply a much larger variability than the actual 0.04 for n = 100, given p = 0.2.
- Option "None of the alternative answers is correct.": Since there is a correct option, this statement is false.

Additional note: Since the population is treated as infinite, there is no need to apply a finite population correction factor; the standard formula for the standard deviation of p̂ applies directly here.

Similar Questions

A sample of 51 observations will be taken from an infinite population. The population proportion equals .85. The probability that the sample proportion will be between .9115 and .9645 is _____.

A sample of size 200 is to be taken at random. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is:随机抽取 200 号样本。假设总体比例为 0.60，则样本比例大于 0.58 的概率为：

It is known that 40% of voters in a certain electorate are in favour of a particular candidate. If a sample of size 30 is taken, what is the probability that less than 35% are in favour of this political candidate?

Suppose 38% of doctors think their patients receive unnecessary medical care and a sample of 300 doctors were taken. What is the probability that the sample proportion will be within ± 3 % of the population proportion?

A sample of 51 observations will be taken from an infinite population. The population proportion equals .85. The probability that the sample proportion will be between .9115 and .9645 is _____.

A population proportion is .75. A random sample of size 100 will be taken and the sample proportion will be used to estimate the population proportion. What is the probability that the sample proportion will be within +/- .03 of the population proportion?

Pew Research says only 40% of Americans plan to get a COVID vaccine. If this is the true population proportion, and a random sample of 100 are asked if they will get a COVID vaccine, what is the probability of 50% or more saying they will?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler