### The Null Hypothesis, Hypothesis Test, Population, Sample, Distribution

The key terms in these Statistic chapters include , The Null Hypothesis, Population, Distribution, Sample Mean, Probability, Sample, Hypothesis, Treatment Effect, Population Mean, Critical Region, Distribution, Linear Regression, Normal Distribution

Which of the following is directly addressed by the null hypothesis?

a) the population before treatment**b) the population after treatment**

c) the sample before treatment

d) the sample after treatment

A hypothesis test involves a comparison of which two elements?

**a) research results from a sample and a hypothesis about a population**

b) research results from a population and a hypothesis about a sample

c) research results from a population and a hypothesis about the population

d) research results from a sample and a hypothesis about the sample

Which of the following accurately describes a hypothesis test?

a) a descriptive technique that allows researchers to describe a sample

b) a descriptive technique that allows researchers to describe a population**c) an inferential technique that uses the data from a sample to draw inferences about a population**

d) an inferential technique that uses information about a population to make predictions about a sample

For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?

a) if there is a treatment effect, it will increase the scores

b) if there is a treatment effect, it will decrease the scores**c) if there is a treatment effect, it will add (or subtract) a constant to each score**

d) if there is a treatment effect, it will multiply (or divide) each score by a constant

A linear regression equation has b = 3 and a = – 6. What is the predicted value of Y for X = 4?

**Ŷ = 6**

Which of the following is directly addressed by the null hypothesis?

a) the population before treatment**b) the population after treatment**

c) the sample before treatment

d) the sample after treatment

A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (Ho) say about the treatment?

a) the treatment causes a change in the scores

b) the treatment adds a constant to each score

c) the treatment multiplies each score by a constant**d) the treatment has no effect on the scores**

A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternate hypothesis (H1) say about the treatment?

**a) the treatment causes a change in the scores**

b) the treatment adds a constant to each score

c) the treatment multiplies each score by a constant

d) the treatment has no effect on the scores

Which of the following accurately describes the critical region?

**a) outcomes with a very low probability if the null hypothesis is true**

b) outcomes with a high probability if the null hypothesis is true

c) outcomes with a very low probability whether or not the null hypothesis is true

d) outcomes with a high probability whether or not the null hypothesis is true

The null hypothesis predicts a specific value for the population mean.

**True**

With a = .05, how are the boundaries for the critical region determined?

**a) boundaries are drawn so there is 2.5% (.025) in each tail of the distribution**

b) boundaries are drawn so there is 5% (.05) in each tail of the distribution

c) boundaries are drawn so there is 10% (.10) in each tail of the distribution

d) boundaries are drawn so there is 5% (.05) in the center of the distribution

If a hypothesis test produces a z-score in the critical region, what decision should be made?

a) reject the alternative hypothesis

b) fail to reject the alternative hypothesis**c) reject the null hypothesis**

d) fail to reject the null hypothesis

A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (Ho) say about the treatment?

a) the treatment causes a change in the scores

b) the treatment adds a constant to each score

c) the treatment multiplies each score by a constant**d) the treatment has no effect on the scores**

The null hypothesis predicts a specific value for the population mean.

**True**

In general, the null hypothesis states that the treatment has no effect on the population mean.

**True**

The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment).

**False**

In most situations, researchers would like the hypothesis test to reject the null hypothesis.

**True**

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

**True**

If a hypothesis test leads to rejecting the null hypothesis, it means that the sample data failed to provide sufficient evidence to conclude that the treatment has an effect.

**False**

If the sample data are in the critical region with a = .05, then the same sample data would still be in the critical region if a were changed to .01.

**False**

If the sample data are in the critical region with a = .01, then the same sample data would still be in the critical region if a were changed to .05.

**True**

A sample of n = 25 individuals is selected from a population with u = 80, and a treatment is administered to the sample. What is the expected if the treatment has no effect?

a) the sample mean should be very different from 80 and should lead you to reject the null hypothesis

b) the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis

c) the sample mean should be close to 80 and should lead you to reject the null hypothesis**d) the sample mean should be close 80 and should lead you to fail to reject the null hypothesis**

Which of the following is an accurate definition of a Type I error?

a) rejecting a false null hypothesis**b) rejecting a true null hypothesis**

c) failing to reject a false null hypothesis

d) failing to reject a true null hypothesis

The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment).

**False**

In most situations, researchers would like the hypothesis test to reject the null hypothesis.

**True**

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

**True**

A linear regression equation has b = 3 and a = – 6. What is the predicted value of Y for X = 4?

**Ŷ = 6**

Which of the following actions would have the effect of either changing the size or direction (sign) of a Pearson r value pertaining to a set of X and Y scores?

**Multiplying each X and Y score by a negative constant value**

A population is normally distributed with µ = 145 and σ = 20. Which is the percentile rank for X = 171?

**90.32% (body)**

A researcher tests their new treatment for sleep disorder among an individual that has a sleep disorder. The researcher knows that individuals diagnosed with sleep disorder tend to have sleep quality scores that form a normal distribution with µ = 40 and σ = 6. The researcher finds that this individual has a sleep quality score of X = 53 following treatment. Which is the probability that a score this large or larger would be obtained if the new treatment had no effect?

**p = 0.0150 (tail)**

A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 34, which proportion of the scores are on the left side of the line?

**0.2743**

What is the probability of randomly selecting a z-score greater than z = -0.75 from a normal distribution?

**p = 0.7734 (body)**

A normal distribution has µ = 20 and σ = 4. Which is the probability of randomly selecting a score greater than X = 25 from this distribution?

**p = 0.1056**

Which statement accurately describes the proportions in the tails of a normal distribution?

**Proportions in both the left-hand and right-hand tails tend to be relatively small.**