Question 1

According to the Central Limit Theorem, what happens to the sampling distribution of the mean as the sample size $$N$$ increases?

Accepted Answer

It approaches a normal distribution with mean $$\mu$$ and variance $$\$$sigma^2$$/N.$$

Question 2

A hospital administrator wants to estimate the average stress score of nurses. The population mean is 50 and the standard deviation is 10. If a sample of 36 nurses is taken, what is the standard error of the mean?

Accepted Answer

$$10/\sqrt{36} = 1.667$$

Question 3

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a null hypothesis when it is true.

Question 4

A researcher sets the significance level at $$\alpha = 0.05. $$What does this mean in terms of risk?

Accepted Answer

There is a 5% chance of rejecting a true null hypothesis.

Question 5

If the population standard deviation is $$\sigma = 8,850$$ and a sample of $$n = 20$$ nurses is taken, what is the standard error of the mean?

Accepted Answer

$$8,850/\sqrt{20} \approx 1,978$$

Question 6

A sample mean salary for unionized nurses is $$76,503$$ with a standard deviation of $$8,850. $$What is the probability that a randomly selected nurse earns more than $$100,000$$?

Accepted Answer

$$P(z \u003e 2.66) = 0.0039$$

Question 7

Which of the following statements about statistical significance is TRUE?

Accepted Answer

Statistical significance can only be interpreted in the context in which it occurred.

Question 8

What is the formula for the Z-score of a sample mean in a sampling distribution?

Accepted Answer

$$Z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n}}$$

Question 9

A sample of 36 nurses has a mean stress score of 50 and a standard deviation of 10. What is the probability that the sample mean falls between 45 and 55?

Accepted Answer

$$P(45 \u003c \bar{x} \u003c 55) = 0.9974$$

Question 10

Which step comes FIRST in the process of statistical inference?

Accepted Answer

Select representative samples.

Question 11

What is the main difference between a Z-score for a single value and a Z-value for a sampling distribution?

Accepted Answer

A Z-score is for individual scores, while a Z-value for a sampling distribution is for sample means.

Question 12

If you want to be 99% confident in your estimate of a population mean, what multiplier should you use for the standard deviation?

Accepted Answer

$$2.56$$

Question 13

Which of the following increases the power of a statistical test?

Accepted Answer

Increasing the sample size.

Question 14

A sample of 20 nurses has a mean annual salary between $$70,000$$ and $$80,000. $$Given a population mean of $$76,503$$ and standard deviation of $$8,850$$, what is the probability that the sample mean falls in this range?

Accepted Answer

$$0.961$$

Question 15

Which of the following is NOT a step in deciding what statistical test to use?

Accepted Answer

Ignore the type of data collected.

Question 16

What does a Type II error represent in hypothesis testing?

Accepted Answer

Accepting a null hypothesis when it is false.

Question 17

Which formula gives the 95% confidence interval for a sample mean?

Accepted Answer

$$	ext{Score} \pm 1.96 	imes 	ext{standard deviation}$$

Question 18

Why is it important to control all other factors when testing for statistical significance between groups?

Accepted Answer

To ensure that any observed difference is due to systematic influence rather than chance.

Question 19

Which of the following statements about sampling distributions is correct?

Accepted Answer

As sample size increases, the sampling distribution of the mean approaches normality.

Central Limit Theorem, Sampling Distributions, and Statistical Significance: Study Notes

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