### Reject The Null Hypothesis, The Probability, Hypothesis – Statistical Test

The key terms in these Statistic chapters include The Probability, Hypothesis, Type I Error, Sample, Alpha Level, Reject The Null Hypothesis, Two-Tailed Test, Population, Normal Distribution, Sample Mean, The Null Hypothesis, Proportion, Two-Tailed Hypothesis, Distribution, Treatment Effect, Z-Score.

You can reduce the risk of a Type I error by using a larger sample.

**True**

The alpha level determines the risk of a Type I error.

**True**

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

**True**

A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect.

**False**

A Type II error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

**True**

The alpha level determines the risk of a Type I error.

**True**

You can reduce the risk of a Type I error by using a larger sample.

**True**

There is always a possibility that the decision reached in a hypothesis test is incorrect.

**True**

A two-tailed hypothesis is being used to evaluate a treatment effect with a = .05. If the sample data produce a z-score of z = -2.24, what is the correct decision?

a) reject the null hypothesis and conclude that the treatment has no effect**b) reject the null hypothesis and conclude that the treatment has an effect**

c) fail to reject the null hypothesis and conclude that the treatment has no effect

d) fail to reject the null hypothesis and conclude that the treatment has an effect

If a hypothesis test rejects the null hypothesis using an alpha level of a = .05, then the research report would include the statement, “p > .05”.

**False**

In a research report, p < .05 indicates that the probability of a Type I error is less than .05.

**True**

In a research report, the term significant result means that the null hypothesis was rejected.

**True**

If other factors are held constant, then increasing the sample size will increase the likelihood of rejecting the null hypothesis.

**True**

A researcher evaluates a treatment effect using a two-tailed hypothesis test with a = .05, and the decision is to reject the null hypothesis. If the researcher switched to a one-tailed test using the same sample, what decision would be made?

**a) definitely reject the null hypothesis with a = .05 and maybe reject with a = .01**

b) definitely reject the null hypothesis with a = .05 and with a = .01

c) definitely fail to reject the null hypothesis with either a = .05 or with a = .01

d) it is impossible to predict the outcome of the one-tailed test

A researcher evaluates a treatment effect using a one-tailed hypothesis test with a = .05, and the decision is to reject the null hypothesis. If the researcher switched to a two-tailed test using the same sample, what decision would be made?

a) definitely reject the null hypothesis with either a = .05 or with a = .01

b) definitely reject the null hypothesis with a = .05 and maybe reject with a = .01**c) might reject the null hypothesis with a = .05 but might not**

d) definitely fail to reject the null hypothesis with either a = .05 or with a = .01

If the research prediction is that the treatment will decrease scores, then the critical region for a directional test will be in the left-hand tail.

**True**

The alpha level determines the risk of a Type I error.

**True**

You can reduce the risk of a Type I error by using a larger sample.

**True**

There is always a possibility that the decision reached in a hypothesis test is incorrect.

**True**

A two-tailed hypothesis is being used to evaluate a treatment effect with a = .05. If the sample data produce a z-score of z = -2.24, what is the correct decision?

a) reject the null hypothesis and conclude that the treatment has no effect**b) reject the null hypothesis and conclude that the treatment has an effect**

c) fail to reject the null hypothesis and conclude that the treatment has no effect

d) fail to reject the null hypothesis and conclude that the treatment has an effect

If a hypothesis test rejects the null hypothesis using an alpha level of a = .05, then the research report would include the statement, “p > .05”.

**False**

In a research report, p < .05 indicates that the probability of a Type I error is less than .05.

**True**

In a research report, the term significant result means that the null hypothesis was rejected.

**True**

A researcher administers a treatment to a sample from a population with a mean of u = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that u >/= 60.

**False**

A researcher is evaluating a treatment that is expected to increase scores. If a one-tailed test with a = .05 is used, then the critical region consists of z-scores less than -1.65.

**False**

The value obtained for Cohen’s d is independent of the sample size.

**True**

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

**True**

A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect.

**False**

A Type II error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

**True**

It is possible for a very small treatment effect to be a statistically significant treatment effect.

**True**

Although the size of the sample can influence the outcome of a hypothesis test, it has little or no influence on measures of effect size.

**True**

Which of the following is an accurate definition for the power of a statistical test?

a) the probability of rejecting a true null hypothesis

b) the probability of supporting true null hypothesis**c) the probability of rejecting a false null hypothesis**

d) the probability of supporting a false null hypothesis

Which of the following will increase the power of a statistical test?

a) change a from .05 to .01

b) change from a one-tailed test to a two-tailed test**c) change the sample size from n = 25 to n = 100**

d) none of the other options will increase power

The power of a hypothesis test is the probability that the sample mean will be in the critical region even if the treatment has no effect.

**False**

If the power for a hypothesis test is calculated to be 0.80, then for same test, the probability of a Type II error is 0.20.

**True**

If all other factors are held constant, increasing the sample size from n = 25 to n = 100 will increase the power of a statistical test.

**True**

It is possible for a very small treatment effect to be a statistically significant treatment effect.

**True**

Although the size of the sample can influence the outcome of a hypothesis test, it has little or no influence on measures of effect size.

**True**

Which of the following is an accurate definition for the power of a statistical test?

a) the probability of rejecting a true null hypothesis

b) the probability of supporting true null hypothesis**c) the probability of rejecting a false null hypothesis**

d) the probability of supporting a false null hypothesis

Which of the following will increase the power of a statistical test?

a) change a from .05 to .01

b) change from a one-tailed test to a two-tailed test**c) change the sample size from n = 25 to n = 100**

d) none of the other options will increase power

The power of a hypothesis test is the probability that the sample mean will be in the critical region even if the treatment has no effect.

**False**

If other factors are held constant, lowering the alpha level will increase the power of a hypothesis test.

**False**

Betsy is currently completing a school teaching placement in order to become an elementary school teacher. One component of the placement includes evaluations from teachers at the school. Evaluations of student teachers are normally distributed with µ = 100 and σ = 12. Betsy is informed that she must score within the interquartile range of this distribution on her evaluations in order to be certified as an elementary school teacher. Which scores encompass the range that Betsy may score to successfully become certified as an elementary school teacher?

**Find z score for both****z= -0.67 x = zσ + µ=91.91 (92); z= 0.67 x = zσ + µ= 108.09 (108)**

Which proportion of a normal distribution is located between z = -1.75 and z = +1.75?

**0.9198**

A class consists of 10 male students and 30 female students. If one student is randomly selected from the class, what is the probability of selecting a male student?

**p = 10/40**

Which proportion of a normal distribution is located in the tail above z = +1.50?

**0.0668**

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

**Body proportions are always ≥ .50.**

A population is normally distributed with µ = 86 and σ = 12. For this population, what is the 78 th percentile?

**X = 95.24**

Delores must grade a driver’s test completed by a group of training students. She knows that driver’s test scores are normally distributed with µ = 50 and σ = 6. Students are required to score in the top 75% of students on the test in order to pass the test and continue on with the training course. Which score do students need to obtain at a minimum in order to pass the test and continue with the course?

**X = 46**

What is the probability of randomly selecting a z-score less than z = -1.55 from a normal distribution?

**p = 0.0606**

A normal distribution has a mean of µ = 50 with σ = 6. If one score is randomly selected from this distribution, which is the probability that the score will be greater than X = 46?

**p = 0.7486**

A researcher evaluates a treatment effect using a two-tailed hypothesis test with a = .05, and the decision is to reject the null hypothesis. If the researcher switched to a one-tailed test using the same sample, what decision would be made?

**a) definitely reject the null hypothesis with a = .05 and maybe reject with a = .01**

b) definitely reject the null hypothesis with a = .05 and with a = .01

c) definitely fail to reject the null hypothesis with either a = .05 or with a = .01

d) it is impossible to predict the outcome of the one-tailed test

A researcher evaluates a treatment effect using a one-tailed hypothesis test with a = .05, and the decision is to reject the null hypothesis. If the researcher switched to a two-tailed test using the same sample, what decision would be made?

a) definitely reject the null hypothesis with either a = .05 or with a = .01

b) definitely reject the null hypothesis with a = .05 and maybe reject with a = .01**c) might reject the null hypothesis with a = .05 but might not**

d) definitely fail to reject the null hypothesis with either a = .05 or with a = .01

If the research prediction is that the treatment will decrease scores, then the critical region for a directional test will be in the left-hand tail.

**True**

The value obtained for Cohen’s d is independent of the sample size.

**True**

Which proportion of a normal distribution is located in the tail above z = +1.50?

**0.0668**

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

**Body proportions are always ≥ .50.**

Which proportion of a normal distribution is located between z = -1.75 and z = +1.75?

**0.9198**

In a research report, p < .05 indicates that the probability of a Type I error is less than .05.

**True**

In a research report, the term significant result means that the null hypothesis was rejected.

**True**

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

**True**

A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect.

**False**

A Type II error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.