Statistics: Exam 2

A measure of the size of an effect in a population is called

Effect size

What is the z score for scores in the top 2.5%?

1.96

A researcher determines that students are active about 60±12 (M−SD) minutes per day. Assuming these data are normally distributed, what is the z score for students being active 48 minutes per week?

-1.0

A researcher determines that students study an average of 80±20 minutes per week. Assuming these data are normally distributed, what is the z score for students studying 60 minutes per week?

-1.0

What is the z score for scores in the bottom 10%?

-1.28

What is the z score for scores in the bottom 5%?

-1.645

A researcher records the following number of birdcalls made during an experimental session with robins: 7.2±0.6 (M±SD). Assuming these data are normally distributed, what is the probability that robins made more than 9 birdcalls during this experimental session?

.0013

What is the typical level of significance for a hypothesis test in behavioral research?

.05

A researcher increases the sample size which will

Decrease the value of standard error

As sample size increases, the standard error of the mean

Decreases

A researcher records the following response times to a visual stimulus: 23±3.1 (M±SD) seconds. Assuming these data are normally distributed, what is the probability that participants responded in 20 seconds or less?

.1660

A researcher has participants choose between three advertisements. She finds that 54 prefer Ad A, 86 prefer Ad B, and 60 prefer Ad C. The probability of proportion of participants preferring Ad B is

.43

Which of the following is a possible value for the standard deviation of a normal distribution: -∞ 0 -2 .5

.5

A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is

.50

A researcher records the following body mass index (BMI) scores for a group of participants: 28.4±1.6 (M±SD). Participants who score between 25 and 30 on this scale are categorized as overweight. What percentage of participants fell in this category?

.8247

A counselor records the number of disagreements (per session) among couples during group counseling sessions. If the number of disagreements is distributed normally as 4.4±0/4 (M±SD) disagreements, then what proportion of couples disagree at least 4 times during each counseling session?

.8413

A researcher measures the number of tasks completed by participants during a 5-minute multitasking session. If the number of tasks completed normally as 6.3±1.0 (M±SD) tasks, then what is the probability that participants completed less than 8 tasks?

.9554

The standard normal distribution is normally distributed with a mean of ____ and a variance of _____

0;1

A professor finds that the students scored a 76±8 (M±SD) on the final exam. On this exam, a score of 90 is an A. Assuming these data are normally distributed, what is the z score for 90 (the cutoff for an A)?

1.75

A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for, say, candidate A equals

1/3

A researcher records the following times (in seconds) that it took a group of students to complete an exam: 18±2 minutes (M±SD). How long did it take 80% of students to complete the exam?

19.68 minutes

A researcher records the following times (in seconds) that it took a group of mice to complete a maze: 23±4.1 (M±SD). The top 10% of mice finishing with the fastest times will be placed in a "maze bright" group. What is the cutoff time to be placed in this group?

28.25 seconds

A researcher records the following assessment data: 42±6 (M±SD). The researcher wants to sample participants scoring in the top 20% of this assessment. What is the cutoff score for the top 20% in this example?

47.04

A professor records the following final exam scores: 78±7 (M±SD). Students scoring in the top 14% get an A. What is the cutoff score for the top 14% in this example?

85.56

A sampling distribution of the sample mean or variance is

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called

A sampling distribution

A researcher records the following time spent sleeping per night (in hours) in a group of participants: 5.8±1.8 (M±SD). The researcher decides to categorize participants who sleep between 6 to 8 hours as moderate sleepers. What percentage of participants fell in this category?

About 35%

A theoretical distribution that evenly distributes data around the mean, median, and mode is called the: -Normal distribution -Bell-shaped distribution -Gaussian distribution -All of the above

All of the above

By definition, the probability of an outcome or event is -The proportion of times an outcome is likely to occur -The fraction of times an outcome is likely to occur -Particularly useful for predicting the likelihood of random events -All of the above

All of the above

If the value of the test statistic is in the rejection region, then -p<.05 -The decision is to reject the null hypothesis -The value of the test statistic is larger than the critical value -All of the above

All of the above

In a normal distribution, 50% of all data: -Fall above the mean -Fall below the median -Fall above and below the mode -All of the above

All of the above

In hypothesis testing, a researcher's decision -Is based on probability -Depends on the level of significance for a hypothesis test -Can be to retain or reject the null hypothesis -All of the above

All of the above

In terms of characterizing samples, statistical theory was developed using a sampling strategy in which -The order of selecting participants matters -The same participant can be selected twice in the same sample -Participants are replaced after being sampled -All of the above

All of the above

Researchers state a level of significance in terms of an alpha level. The alpha level indicates -The probability of committing a Type I error -The probability of incorrectly rejecting the null hypothesis -The probability value for the rejection region -All of the above

All of the above

Which of the following is a scenario in which increasing sample size will increase power? -When the effect size is small -When the effect size is large -When the probability of a Type I error is small -All of the above

All of the above

The probability of committing a Type I error is stated by ____________; the probability for committing a Type II error is stated by _________

Alpha; beta

Most behavior is believed to __________ a normal distribution

Approximate

Which of the following is required to locate proportions of area under the normal curve? -Compute a z-transformation -Find the probability of a z score in the unit normal table -Both A and B -None of the above

Both A and B

Which of the following is required to locate z scores with a given proportion? -Find the z score associated with a given probability -Compute a z-transformation to find the raw score -Both A and B -None of the above

Both A and B

Regardless of the distribution of the population, the sampling distribution means will be approximately normally distributed. What characteristic of the mean explains this?

Central limit theorem

The one-sample z test is a hypothesis test used to test hypotheses

Concerning a single population with a known variance

Which of the following is not a step to locate a proportion in a normal distribution? -Transform a raw score (x) into a z score -Locate the corresponding proportion for the z score in the unit normal table -Convert a proportion to a standard normal z score

Convert a proportion to a standard normal z score

When reporting the results of a one-sample z test using APA format, the ___________ does not need to be reported

Critical values

__________ allows researchers to describe (1) how far mean scores have shifted in the population, or (2) the percentage of variance that can be explained by a given variable

Effect size

The mean of the sampling distribution of sample means is

Equal to the population mean

A researcher visits a population of 1,200 local residents to determine the proportion of local residents who support a new smoking ban. In this case, the sample space is

Equal to the total number (or population) of residents

Which of the following is not one of the four steps to hypothesis testing -State the hypothesis -Evaluate the plan -Set the criteria for a decision -Compute the test statistic

Evaluate the plan

A researcher finds that the average preschool-aged child drinks two cups of milk per day. Assuming these data are normally distributed, the z score for the average cups per day in this example is

Exactly equal to 0

Which type of sampling is most often applied by researchers in the behavioral sciences?

Experimental sampling

A researcher obtains z=3.98 for a one-sample z test. If her decision is to retain the null hypothesis, then what do you know about her decision?

Her decision resulted in a Type III error

A method for testing the claim or hypothesis about a parameter in a population, using data measured in a sample, is called

Hypothesis testing

What does it mean to say that the sample mean is an unbiased estimator of the population mean?

If we select a sample at random, then on average we can expect the sample mean to equal the population mean

Increasing sample size will

Increase the power of the decision

A researcher conducts a study, but has low power to detect an effect. Which of the following is one way in which the research can increase power?

Increase the sample size

It happens to be the case that the standard error of the sampling distribution of sample means

Is minimal

A researcher obtains z=1.80 for a one-sample z test. What is the decision for this test at a .05 level of significance

It depends on whether the test is one-tailed or two-tailed

What is the central limit theorem?

It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population

Which of the following best describes the p value?

It is a conditional probability

Based on the effect size conventions, d=0.99 is a

Large effect size

The criteria for a decision regarding the value stated in a null hypothesis is set by the

Level of significance

A researcher believes that increasing attention given to children will improve mean academic performance. Therefore, the alternative hypothesis should be

Mean academic performance will increase

A researcher reports that the size of an effect in some population is d=0.88. Which of the following is an appropriate interpretation for d?

Mean scores shifted 0.88 standard deviations in the population

Based on the effect size conventions, d=0.60 is a

Medium effect size

A parent decides to reward her child if he eats an average of at least five bites of his vegetables at dinner during the first week. She finds that her child ate 4±0.8 (M±SD) bites per meal for the first week. Assuming these data are normally distributed, should this parent reward her child?

No, because the z score for 5 bites is greater than 0.

A researcher reports the following result for a one-sample z test at a .05 level of significance: z=1.88, p=.06 (d=.25). Is this result significant?

No, the decision is to retain the null hypothesis

Two normal distributions are observed. The first distribution has a mean of 12 and a standard deviation of 2. The second distribution has a mean of 0 and a standard deviation of 2. For which distribution will the z score for the mean be larger?

None, the z score will be the same

The following distribution most closely approximates a

Normal distribution

Is a one-sample z test reported differently for one-tailed and two-tailed tests?

Not, the same values are reported

Suppose you select a sample of tree people from a population of four (A, B, C, D). Which of the following samples is possible using the experimental sampling strategy?

Persons B, C, and D

A researcher reports that the standard deviation in Population A is σ=2.3 and the standard deviation in Population B is σ=4.3. Which population is associated with the highest power to detect an effect

Population A

A researcher reports that the size of an effect in Population A is d=0.10 and the effect size in Population B is d=0.34. Which population is associated with greater power to detect an effect?

Population B

The proportion or fraction of times an outcome is likely to occur is referred to as

Probability

Which of the following is NOT a characteristic of probability? -Probability varies between 0 and 1 -Probability can never be negative -Probability can be stated as a fraction or decimal -Probability is most useful for describing fixed events

Probability is most useful for describing fixed events

In hypothesis testing, a researcher can never

Prove that his or her hypothesis is correct

A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and a standard deviation of 12. She determines that the mean IQ in this sample is 104. Assuming she computes a one-sample z test at a .05 level of significance, what is the decision for a two-tailed test?

Reject the null hypothesis; IQ scores in this sample are significantly higher than those in the copulation

In step 2 of hypothesis testing, researchers state a level of significance to minimize the probability of

Rejecting a true null hypothesis

The normal distribution is symmetrical, which means that

Scores above the mean are distributed the same as scores below the mean

Suppose a researcher wants to make sure that the probability of committing a Type I error is less than 5%. How can the researcher control for this?

Set the level at .05

Hypothesis testing is also called

Significance testing

Based on the effect size conventions, d=0.18 is a

Small effect size

A distribution of z scores are distributed in what type of unit of measurement?

Standard deviation units

The __________ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and a variance of 1.

Standard normal transformation

The first step to hypothesis testing requires that a researcher

State the hypotheses

A researcher conducts two studies. Each study was a one-sample z test. Both studies placed the rejection region in both tails and measured the same sample mean. The alpha level in Study 1 was larger than the alpha level used in Study 2. Which study is associated with greater power to detect an effect?

Study 1

Scores far from the mean are located in the _______ of a normal distribution

Tails

What is the implication for the tails of a normal distribution being asymptotic?

That extreme scores are possible in the normal distribution

Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means?

The central limit theorem

A researcher computes a one-sample z test in two studies. Both studies used the same alpha level, placed the rejection region in both tails, and measured the same sample mean. The researcher selects a sample of 30 participants in Study 1 and decides to retain the null hypothesis. She selects a sample of 60 participants in Study 2 and decides to reject the null hypothesis. Which of the following is the best explanation for why the decision was different in Study 1 and study 2?

The different decisions in Study 1 and Study 2 are possible because the second test was associated with greater power to detect an effect

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z=1.00, or the area to the left of z=-1.oo

The first area is bigger

The power of the decision-making process is

The likelihood of rejecting a false null hypothesis

Which of the following statements regarding the null hypothesis is true?

The null hypothesis always makes statements about a population parameter

A researcher reports that scores were higher than the mean in the population, z=1.60, p=.05 (d=.14). If this was a test at a .05 level of significance, then what value must be incorrectly reported?

The p value

Which proportion is largest in a z distribution?

The proportion of area between z=+1 and z=-1

Experimental research is typically conducted using a sampling strategy in which

The same participant can never be selected twice in the same sample

The total number of possible outcomes for a random variable is referred to as

The sample space

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the right of the mean, or the area between z=±1.00

The second area is bigger

The normal distribution has all of the following characteristics, except that -It is symmetrical -Its distribution is theoretical -The total area under the curve is greater than 1.0 -The mean, median, and mode are equal

The total area under the curve is greater than 1.0

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z=0.80, or the area to the right of z=-0.80

The two areas are the same

The mean can take on any value and the standard deviation can take on any positive value. Therefore,

There are an infinite number of possible normal distributions

A researcher computes a test statistic and finds that the p value for this test is .03. What does this result mean?

There is a 3% likelihood of obtaining the test statistic value, if the null were true

If a researcher obtains a null finding, then what is the decision?

They correctly retained the null hypothesis

A researcher obtains z=2.04 for a one-sample z test. What is the decision for this test at a .05 level of significance?

To reject the null hypothesis

Given the following values: µ=10, M=8, σM-0.5, conduct a one-sample z test at a .05 level of significance. What is the decision for a two-tailed test?

To reject the null hypothesis

A professor finds that the average SAT score among all students attending his college is 1150±150 (µ±σ). He polls his class of 25 students and finds that the average SAT score is 1200. Suppose he computes a one-sample z test at a .05 level of significance. What is his decision?

To reject the null hypothesis for an upper-tailed test, but to retain the null hypothesis for a two-tailed test

What are the two decisions that researchers can make in hypothesis testing?

To retain or reject the null hypothesis

A researcher obtains z=-6.45. What is the decision for a one-tailed test, upper-tail critical, at a .05 level of significance?

To retain the null hypothesis

A researcher obtains z=1.45 for a one-sample z test. What is the decision for this test at a .05 level of significance?

To retain the null hypothesis

Given the following values: µ=6.0, M=7.6, n=36, σ=6, conduct a one-sample z test at a .05 level of significance. For a one-tailed test, upper-tail critical, what is the decision?

To retain the null hypothesis

Which of the following is not a step to locate a score in a normal distribution? -Locate a z score associated with the given proportion in the unit normal table -Transform the z score into a raw score (x) -Transform a raw score (x) into a z score

Transform a raw score (x) into a z score

A researcher directly controls for the probability of a _________, but does not directly control for the probability of a __________

Type I error; Type II error

When a researcher decides to retain the null hypothesis because the rejection region was located in the wrong tail, this is called a

Type III error

A researcher randomly selects a sample of athletes and reports that their average score on a health and fitness scale is 23. Based on the characteristics of the sample mean, what does this say about the mean in the population?

We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean

A therapist has a goal to reduce the mean number of patient symptoms expressed for a particular disorder to two symptoms per day. Following therapy, she determines that the z score for 2 symptoms per day is 0. Assuming the data are normally distributed, did she reach her goal?

Yes, because a z score of 0 is the average, or mean

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a

z score

What is the z score for scores in the top and bottom 2.5%?

±1.96

A professor gives an exam in which the mean score is 78 points. She gives another exam to test whether or not scores change. In this example, the null hypothesis is

µ=78