Q: A company wants to estimate the proportion of customers who prefer online shopping. If the true proportion is $$p = 0.3$$ and a random sample of $$n = 100 is $$taken, what is the standard deviation of the sample proportion?

$$\sqrt{\frac{0.3 \times 0.7}{100}}$$

Q: A survey of 1000 randomly selected customers finds that 30% prefer a new product. What is the standard error of the sample proportion?

$$\sqrt{\frac{0.3 \times 0.7}{1000}}$$

Question 1

Which of the following best describes the Central Limit Theorem (CLT) as it applies to business statistics?

Accepted Answer

The distribution of a sample mean becomes approximately Normal as the sample size increases, regardless of the population's distribution.

Question 2

A company wants to estimate the proportion of customers who prefer online shopping. If the true proportion is $$p = 0.3$$ and a random sample of $$n = 100 is $$taken, what is the standard deviation of the sample proportion?

Accepted Answer

$$\sqrt{\frac{0.3 	imes 0.7}{100}}$$

Question 3

Which of the following is NOT an assumption or condition required for the sampling distribution of the sample proportion to be approximately Normal?

Accepted Answer

The population must be Normally distributed.

Question 4

Suppose the weights of shipments are unimodal and symmetric with mean $$\mu = 12 kg $$and standard deviation $$\sigma = 4 kg. If a $$pallet contains 10 boxes, what is the standard deviation of the sample mean weight?

Accepted Answer

$$\frac{4}{\sqrt{10}}$$

Question 5

A sample of 100 customers is taken from a population where $$p = 0.2. $$What is the mean of the sampling distribution of the sample proportion?

Accepted Answer

$$0.2$$

Question 6

Which of the following best explains why the sample proportion is considered an unbiased estimator of the population proportion?

Accepted Answer

The mean of the sampling distribution of the sample proportion equals the true population proportion.

Question 7

If a population is not Normal but the sample size is large, what does the Central Limit Theorem tell us about the sampling distribution of the sample mean?

Accepted Answer

It will be approximately Normal.

Question 8

A business analyst collects a random sample of 50 sales transactions. The sample mean is $$\bar{y} = 200$$ and the sample standard deviation is $$s = 40. $$What is the standard error of the mean?

Accepted Answer

$$\frac{40}{\sqrt{50}}$$

Question 9

Which of the following is a correct interpretation of 'sampling error' in the context of business statistics?

Accepted Answer

The natural variability in sample statistics from one sample to another.

Question 10

A survey of 1000 randomly selected customers finds that 30% prefer a new product. What is the standard error of the sample proportion?

Accepted Answer

$$\sqrt{\frac{0.3 	imes 0.7}{1000}}$$

Question 11

Which of the following conditions must be checked before using the Normal model for the sampling distribution of the sample mean?

Accepted Answer

Independence, randomization, 10% condition, and large enough sample size.

Question 12

A manager wants to know the probability that the mean weight of 10 randomly selected boxes exceeds 15 kg, given $$\mu = 12 kg $$and $$\sigma = 4 kg. $$What is the z-score for this scenario?

Accepted Answer

$$\frac{15 - 12}{4/\sqrt{10}}$$

Question 13

If the sample size is increased in a survey, what happens to the standard deviation of the sampling distribution of the sample proportion?

Accepted Answer

It decreases.

Question 14

Which formula would you use to estimate the standard error of the sample mean when the population standard deviation is unknown?

Accepted Answer

$$\frac{s}{\sqrt{n}}$$

Question 15

A sample of size $$n = 100 is $$drawn from a population with $$p = 0.2. $$What is the probability that the sample proportion is more than 0.3? (Use $$SD_{\hat{p}} = 0.04$$ and Normal approximation.)

Accepted Answer

About 0.0062

Question 16

Which of the following best describes the difference between the distribution of a sample and the sampling distribution?

Accepted Answer

The distribution of a sample refers to the values in one sample, while the sampling distribution refers to the distribution of a statistic over many samples.

Question 17

Why is it important for samples to be independent when constructing a sampling distribution?

Accepted Answer

Dependence between samples can bias the estimate and invalidate the model assumptions.

Question 18

If a sample is not randomly selected, which assumption is violated and what is the consequence?

Accepted Answer

Randomization; the sampling distribution may not accurately reflect the population.

week 1-1 ch 10

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