CJ315;Exam2 Chapter 5-8

Suppose you earned a score of X = 54 on an exam. Which set of parameters would give you the highest grade?

μ = 50 and σ = 2

The mean for any distribution corresponds to a z score

0

For any normal distribution, what is the probability of selecting a score less than the mean?

50%

For any distribution the score that separates the highest 10% from the rest of the scores is called the.

90th percentile

Roughly what percentage of scores will fall within +/-2 standard deviations of the mean (above and below)?

95%

Roughly what percentage of scores will fall within +/-3 standard deviations of the mean (above and below)?

99%

As sample size increases, the standard error of M __________.

Decreases

The critical region for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = 1.25, then what is the correct statistical decision?

Fail to reject H0

For any population, a z-score of +1.00 corresponds to a location exactly 10 points above the mean.

False

The distribution of SAT scores is normal with μ = 500 and σ = 100. If a score of 600 or higher is required for admission to the college, then only 84.13% of the students taking the SAT are eligible for admission.

False

Last week Sarah had exams in Math and in Spanish. On the Math exam, the mean was μ = 30 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was μ = 60 with σ = 6 and Sarah had a score of X = 65. For which class should Sarah expect the better grade?

Math

A jar contains 15 red marbles and 75 blue marbles. If you randomly select a marble from this jar, the probability of obtaining a red marble is p = 15/90.

True

A positive z-score always corresponds to a score greater than the mean.

True

As defined in the text, random sampling requires that each individual in the population has an equal chance of being selected

True

Every X value that is less than the population mean will have a negative z-score.

True

For a hypothesis test, the critical region is defined as the set of sample outcomes that is very unlikely to be obtained if the null hypothesis is true.

True

For a normal distribution, all negative z-scores have percentile ranks less than 50%.

True

For any normal distribution, exactly 2.5% of the scores are located in the tail beyond z = 1.96.

True

The distribution of IQ scores is normal with μ = 100 and σ = 15. Less than 5% of the population have IQ scores above 130.

True

The population mean always corresponds to a z-score of zero.

True

The standard error for a sample mean can never be larger than the standard deviation of the population from which the sample is selected.

True

The value for a probability can never be less than zero, unless you have made a computational error.

True

The value for a probability can never exceed 1.00, unless you have made a computational error.

True

Two samples will probably have different means even if they are both the same size and they are both selected from the same population.

True

For the past 20 years, the high temperature on April 15th has averaged μ = 62 degrees with a standard deviation of σ = 8. Last year, the high temperature was 66 degrees. Based on this information, last year's temperature on April 15th was___.

a little above average

In a hypothesis test, an extreme z-score value, like z = +3 or z = +4, __________.

a. is probably in the critical region b. means that you should probably reject the null hypothesis c. is strong evidence of a statistically significant effect d. All of the other options are correct.

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

change the sample size from 25 to 100

A treatment is administered to a sample selected from a population with a mean of μ = 80 and a standard deviation of σ = 10. After treatment, the sample mean is M = 85. Based on this information, the effect size as measured by Cohen's d is __________.

d = 0.50

A Type I error means that a researcher has __________.

falsely concluded that a treatment has an effect

The probability of committing a Type I error __________.

is determined by the level of significance (α) that one chooses

One assumption for a hypothesis test with z-scores is that the distribution of sample means __________.

is normal

A random sample is selected from a population with a standard deviation of σ = 20. If the sample mean has a standard error of 2 points, how many scores are in the sample?

n = 100

Which of the following samples would have the smallest standard error?

n = 100 scores from a population with σ = 10

A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.37. Assuming that the researcher is using a two-tailed test, the researcher should _______________.

reject the null hypothesis with α = .05 but not with α = .01.

In a hypothesis test, the critical region consists of __________.

sample values that are very unlikely to be obtained if H0 is true

A z-score of z = −0.25 indicates a location that is .

slightly below the mean

For a population with μ = 80 and σ = 10, what is the z-score corresponding to X = 85?

+0.50

When a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. On average, the size of the difference between the sample mean and the population mean is predicted by __________.

the standard error

The standard deviation of the distribution of sample means is called __________.

the standard error of M

A researcher reports that there is a significant difference between two treatments at the .05 level of significance. This means that __________.

there is a 5% probability (or less) that the difference occurred simply by chance without any treatment effect

A normal distribution has a mean of μ = 40 with σ = 4. What is the probability of sampling an individual with a score greater than 46?

0.0668

For a normal distribution, which of the following percentiles is located farthest from the mean?

3rd percentile

A population of scores has μ = 50. In this population, an X value of 58 corresponds to z = 2.00. What is the population standard deviation?

4

For a particular population a sample of n = 4 scores has a standard error of 10. For the same population, a sample of n = 16 scores would have a standard error of __________.

5

A hypothesis test is used to evaluate the effect of a treatment. If the test decision is to reject the null hypothesis with α = .05, then there will be ____ chance that the decision is wrong.

5%

For a population with μ = 60 and σ = 8, what is the X value corresponding to z = −0.50?

56

For a normal distribution with μ = 100 and σ = 10, what is the probability of selecting a score less than X = 85?

6.68%

Roughly what percentage of scores will fall within +/-1 standard deviation of the mean (above and below)?

68%

A population of scores has σ = 20. In this population, a score of X = 80 corresponds to z = +0.25. What is the population mean?

75

Which of the following would produce a standard error of 3 points? a. n = 4 scores from a population with σ = 6 b. n = 9 scores from a population with σ = 9 c. n = 16 scores from a population with σ = 12

All three samples would produce a standard error of 3 points.

If there are 10 seniors and 40 juniors in a class, then the probability of randomly selecting one individual who is a senior is p(senior) = 1/4 or 25%.

False

For any normal distribution, the mean and the median will have the same value.

True

For any normal distribution, the proportion corresponding to scores greater than z = +1.00 is exactly equal to the proportion corresponding to scores less than z = -1.00.

True

For any population, a z-score of +1.00 corresponds to a location above the mean by one standard deviation.

True

If a specific sample leads to rejecting the null hypothesis with α = .01, then the same sample would also lead to rejecting the null hypothesis with α = .05.

True

If the data provide convincing evidence that the treatment does have an effect, then the statistical decision is to reject the null hypothesis.

True

If the obtained sample data are not in the critical region, then the correct statistical decision is "fail to reject the null hypothesis."

True

If there are 50 students in a class, then the probability of randomly selecting any particular individual is p = 1/50.

True

If you fail to reject the null hypothesis, it means that the data do not provide sufficient evidence to say that the treatment has an effect.

True

In a research report, the notation p < .05 is used to when the null hypothesis is rejected and the treatment is shown to have a significant effect using an alpha level of α = .05.

True

In a research report, the term statistically significant is used to indicate that the null hypothesis was rejected.

True

In any normal distribution, 80.64% of the scores fall between z-scores of +1.30 and -1.30.

True

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

True

In general, the smaller the variance (or standard deviation), the more likely you are to reject the null hypothesis.

True

In most research situations, the goal is to reject the null hypothesis.

True

In the social sciences, the most commonly used α level for hypothesis testing is .05.

True

Locations near the population mean will have z-scores near zero.

True

Within any distribution of scores, the location specified by z = +1 and the location specified by z = −1 are exactly the same distance from the mean.

True

The distribution of sample means (for a specific sample size) consists of __________.

all the sample means that could be obtained (for the specific sample size)

A hypothesis test is __________.

an inferential technique that uses the data from a sample to draw inferences about a population

The null hypothesis __________.

concerns a population with an unknown mean b. is denoted by the symbol H0 c. generally states that there is no effect, no change, or no difference

A Type II error means that a researcher has __________.

falsely concluded that a treatment has no effect

In N = 25 games last season, the college basketball team averaged μ = 74 points with a standard deviation of σ = 6. In their final game of the season, the team scored 90 points. Based on this information, the number of points scored in the final game was .

far above average

A z-score of z = +3.00 indicates a location that is .

far above the mean in the extreme right-hand tail of the distribution

In general, increasing the alpha level (for example from .01 to .05) will __________.

increase the likelihood of rejecting the null hypothesis

In hypothesis tests, standard error measures __________.

the amount of difference between the sample mean and the population mean that is reasonable to expect just by chance

When the sample size is greater than n = 30 __________.

the distribution of sample means will be approximately normal