Chapter 6

issues related to hypothesis testing

- proof implies certainty/probability; hypothesis testing can only provide support or lack of support for a hypothesis

Four steps to hypothesis testing

1. State the null and alternative hypotheses (H0 and H1) - Null: (proposes that the hypothesized change does not exist) - example: football coin toss result does not effect outcome of game (H0: x=6) -Alternative hypotheses: (proposes that the hypothesized change does exist) - example: football coin toss result does effect outcome of game (H1: x does not = 6) 2. Make a decision about null hypothesis - Look for evidence that has a low probability - 5% chance of the statistic occurring when null hypothesis is true = low probability 3. Draw a Conclusion... it should state: - the sample from whom the data were collected -the value of the statistic calculated from the data -the decision about the null hypothesis -the probability of the statistic 4. Relate the result of the analysis to the research hypothesis - does the statistical analysis support the original research hypothesis?

Factors that affect the decision of accepting or rejecting the null hypothesis (3)

1. sample size - the larger the sample size, the greater the likelihood of rejecting the null hypothesis 2. Alpha - the smaller the value of the mean, the lower the likelihood of rejecting the null hypothesis 3. Directionality of the alternative hypothesis - nondirectional hypotheses: regions of rejection in only one end of the distribution (one-tailed)

Alpha (α) refers to Select one: a. the probability of a statistic needed to reject the null hypothesis b. an example of a population parameter c. the probability of accepting the null hypothesis d. the minimum value of a statistic needed to reject the null hypothesis

A

A researcher finds that the mean number of arrests for juveniles in his sample is .39 whereas the mean number of arrests in the population is .15 The difference between the two means can be attributed to: Select one: a. a lack of planning b. sampling error c. non-normal error d. luck

B

Sampling error refers to: Select one: a. difference between the likelihood of being in one category versus another category. b. differences between statistics calculated from two different populations. c. differences between statistics calculated from a sample and statistics pertaining to the population from which the sample is drawn. d. differences between the likelihood of an occurrence of a particular outcome of an event and all possible outcomes.

C

The term "critical value" is used to define Select one: a. the level of significance of a statistic b. the likelihood of rejecting the null hypothesis c. the minimum value of a statistic needed to reject the null hypothesis d. the probability of a statistic needed to reject the null hypothesis

C

Which of the following beliefs is the best example of an alternative hypothesis (H1)? Select one: a. "The networks of the different cell phone companies are all the same" b. "Girls are just as good at sports as are boys" c. "Taking hormones helps baseball players hit more home runs" d. "There are no weapons of mass destruction in Iraq"

C

You _____ the null hypothesis when the probability of the statistic is ___ 5%. Select one: a. reject; greater than b. accept; less than c. reject; less than d. do not reject; not equal to

C

A decision rule Select one: a. defines what is meant by a "low" probability b. states the null and alternative hypotheses c. specifies when researchers can say their hypothesis has been proved d. specifies the values of a statistic that lead to rejection of the null hypothesis

D

In this figure, if the value of a calculated statistic falls in the _____, you will ______. (A normal curve with a small portion of the right and left side tails shaded) Select one: a. shaded area; not reject the null hypothesis b. shaded area; reject the alternative hypothesis c. unshaded area; reject the null hypothesis d. unshaded area; not reject the null hypothesis

D

The process of hypothesis testing starts with the assumption that Select one: a. the null hypothesis is false b. we do not know whether the null hypothesis or the alternative hypothesis is true. c. the alternative hypothesis is true d. the null hypothesis is true

D

Which of the following beliefs is the best example of a null hypothesis (H0)? Select one: a. "Republicans are more likely to shoot their hunting partners than are Democrats" b. "There is life on Mars" c. "Women are more considerate than men" d. "All politicians are the same"

D

Which of the following is an example of a binomial variable? Select one: a. Race (White, Asian, African American, Hispanic, Native American) b. Religion (Christian, Buddhist, Catholic, Agnostic) c. Highest degree (High school diploma, Some college, BA, professional degree) d. Age (Over 65 or Under 65)

D

Importance of probability

Research is typically conducted with samples rather than populations, researchers rely on probability to evaluate data collected from samples

The sum of the probabilities for the values of a binomial variable equals 1.0. Select one: True False

True

binomial distributions

based on variables with only two categories (male or female) (correct or incorrect) (heads or tails)

Mathematically, probability may be defined as Select one: a. the total number of possible outcomes minus the number of ways a particular outcome may occur. b. the number of ways an outcome may occur. c. the number of ways an outcome may occur divided by the total number of possible outcomes. d. the likelihood of rejecting the null hypothesis.

c

Probability is an important concept for researchers primarily because Select one: a. most research involves flipping coins and pulling aces out of a deck of cards. b. it is used to develop statistical hypotheses such as the null hypothesis and alternative hypothesis. c. it is used to evaluate data collected from samples. d. it is used to prove a study's research hypotheses.

c

Statistical hypotheses

focus on numerical expressions of relationship between variables

Research hypotheses

focus on verbal expression of concepts

the probabilities of outcomes in a binomial distribution become increasingly normal in shape with __________ sample sizes

larger

p(event)=

number of total ways an outcome can occur/total # of possible outcomes

percentages of scores in the normal curve can be re-expressed as _____________ (example)

probabilities - the percentage of scores between z=0 and z=2.24 is the same as the probability that a randomly selected z-score will be between z=0 and z=2.24

sampling error

samples are imperfect representations of a population (must be random)

probability

the likelihood of occurrence of an outcome of an event given all possible outcomes

critical value

value of a statistic that separates the two regions (region of rejection is outside the critical values. If that's where the experimental results end up, you can reject the null hypothesis)

Region of rejection

values of a statistic whose combined probability is low enough to lead to the decision to reject H0 (the tails)

region of non-rejection

values of a statistic whose combined probability is not low enough to lead to the decision to reject H0 (NEVER ACCEPT, just don't reject)