Chapter 5-8

For a normal distribution, the proportion in the tail beyond z= 1.00 is exactly the same as the proportion in the tail beyond z= - 1.00

True

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

True

True

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

The score above the mean x= 75 and M= 60 the distance is 15 points. Has O=12 15/12 = 1.25 It is the same Z= x- m/ o = 75 - 60/12 = 15/12 = 1.25

A distribution score has a mean of M= 60 with a O =12. Find the z= score for x= 75

(True) The z-score distribution will always have a mean of zero.

A population with M=100 and O= 20 is transformed into z -scores. The resulting distribution of z-scores will have a mean of zero.

True

A population with M=37 and a O= 6 in standardized to create a new distribution with M=100 and O =20. In this transformation a score of x= 43 from the original distribution will be transformed into a score of x= 120

True

A score of -2.00 always indicating a more extreme location (farther) from the mean than a z-score of -1.00

There is always some probability that a hypothesis test will lead to the wrong conclusion. Define a type 1 error

A type 1 error is rejecting a true null hypothesis

True

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

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

Change the sample size from 25 to 100

The distribution of sample means

Either criterion is sufficient for a normal distribution. Will be normal if either the population is normal of the sample size is n > 30 --

A sample of n= 25 scores has a standard error of 2. This sample was selected from a population with O=50

False

For any normal distribution a z-score of -1.28 separates the top 10.03% from the rest of the distribution.

False 89.97% have scores greater than z= -1.28

The mean of the distribution of sample mean is called the standard

False error of m, the mean is called the expected value of M.

A population has M= 80 and O=20. The distribution of sample mean based on sample of N= 16 selected from the population will have an expected value of 80/4= 20

False the expected value is M=80. The mean of the distribution is equal to the mean of the population.

If the obtained sample data are in the critical region, then we conclude that the data provide support for the null hypothesis.

False, Large variance lower the likelihood of rejecting the null hypothesis.

If a researcher is predicting that a treatment will produce an increase in scores, then the critical region for a directional test would be located entirely in the left- hand tail of the distribution.

False, large scores (right-hand tail.) indicates that the treatment works.

If a sample consists of at least n= 30 scores, then the sample mean (m) will be equal to the population mean.

False, with a sample size of n=30 or more, the sample mean (m) should be close to M population. mean but probably not equal to M

A population has m= 80 and O= 20. The distribution of sample means based on samples of n= 4 selected from the population will have a standard error of 5

False.

A type 2 error occurs when you conclude that a treatment effect exists, but the treatment has no effect.

False. A type 2 error is concluding that there is no effect when there is.

The score has a mean a M= 66 with a O= 12. Find the Z-score for X=75

Find the z- score for x= 75 the score above the mean x=75 the score above the mean x=75 and m=60 the distance is 15 points. Has O= 12 15/12 = 1.25 It is the same z= x-m/o = 75- 60/12 = 15/12= _1.25

False, the score is below, the mean M=40. standard deviation s= 12 the score is x=34 40-6= 34

For a sample with M=40 and S= 12 a z-score of Z= -0.50 corresponds to a score of x= 46. (1/2) (12) = 12/2= 6

True

For any distribution a z-score of z= -0.50 corresponds to a location below the mean.

True

In a distribution with M = 50 and O= 10, the score of x = 55 corresponds to a z-score of z= 0.50

False X= 70 is below the mean 0.50 S= 80 -70 = 10 distance of 10 points. If one half of the standard deviation is 10 or 1/2= 10 O = 20 standard deviation is 0 =20

In a distribution with M=80, a score of x=70 corresponds to z= -0.50. The standard deviation for the population is O = S

M =60 Z= X-M/S = 64 -60/ 8 = 4/8 = +0.5 False the score is +0.50, the score x=64 is above the mean M=60

In a sample with S= 8 a score of x= 64 corresponds to a z= -0.50 The mean for the sample is

Increasing the alpha level (for example from a= .01 to a =.05) ____

Increases the probability of a type 1 error increases the size of the critical region increases the probability that the sample will fall into the critical region Increasing the alpha expands the critical region and increases the risk go a type 1 error

If the instructor multiplied every score by z, what would happen to your z- score?

Multiplying every score by 2 will multiply the mean, the standard deviation and your score. However your z-score (your position within the distribution) will not change

Which of the following is an advantage of transforming x-values into z-scores?

None of the other options is an advantage. None of these characteristics is associated with z-scores.

a researcher is conducting a hypothesis test to determine whether a treatment produces a significant ant increase in scores. If thew sample data produces a z= +1.89, which of the following conclusion is justified?

Reject Ho using a one-tailed test with O=.05

True

Sampling with replacement means that it is possible for the same individual to be selected more than once for a single sample

True

The definition of a random sample in the text requires sampling with replacement.

The mean of the distribution of sample means is called

The expected value of M. The average value of M is called the expected value

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= 2.77 assuming that the researcher is using a two tailed test

The researcher should reject the null hypothesis with either O=. 05 of O= .01

A sample of n=25 individuals is selected from a population with M=80 and a treatment is administered to the sample. If the treatment has no effect then

The sample mean should be close to 80 and should lead you to fail to reject the null hypothesis.

A very small treatment effect can still be significant if

The sample size (n) is very large

A population has a M= 100 and standard deviation of O= 10. If a single score is randomly selected from this population, how much distance on average should you find between the score and the population mean?

The standard deviation O=10 measures the standard distance between a score and the population mean.

True

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

A hypothesis is test is used to evaluate the effect of a treatment. Of the test decision is tolerant the null hypothesis with O= .05 then _____

There is a 5% chance that the decision is wrong

A researcher obtained M= 27 for a sample of n=36 scores selected from a population with M= 30 and O=12. This sample mean corresponds to a z-score of z=1.50

True

Assuming that all other factors are held constant, as the population variability increases the standard error will also increase

True

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

True

It is possible for the distribution of sample means to be normal even if it is based on samples with less than n=30

True

One way to reduce the risk of a type 1 error is to lower the alpha level

True

The critical region consists of extreme sample values that are very unlikely to occur is the null hypothesis is true

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

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

True

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

True

A jar contains 10 red marbles and 20 blue marbles. If you take a random sample of two marbles from this jar, then the probability that the second marble is blue does not depend on the color of the first marble.

True in random sample, there has to be replacement

Under what circumstances would a score that is 15 points above the mean be considered to be near the center of the distribution

When the population standard deviation is much larger than 15 15 points is a small distance when the standard deviation is more than 15

Describe the consequences of a type 1 error

a researcher concludes that a treatment has an effect which infant it does not this can lead to a false report.

Describe the consequences of a type 2 error

a researcher concludes that the data do not provide a convincing demonstration that the treatment has any effect, when there is an effect. The researcher may choose to refine and repeat the experiment

If the instructor every score, what would happen to your z-score?

adding 5 points to every score would increase your score and the mean by 5 points. However your z-score would not change

A z-score of z= -2.00 indicates a position

below the mean by 2 times the standard deviation The z-score identifies the direct and distance from the mean in terms of the number of standard deviations

As sample size increases, the standard error of M _____

decreases

For any normal distribution, the proportion in the tail beyond z= 2.00 is p = -0.0228

false, proportions are always positive. Cant be negative

A type 1 error means that a researcher has _____

falsely concluded that a treatment has an effect

define a type 2 error

is failing to reject a false null hypothesis

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

is probably in the critical region means that you should probably reject the null hypothesis is strong evidence of a statistically significant effect the critical region is defined by extreme values.

False changing x to Z does not change the shape of the distribution

one advantage of transforming x values into z- scores is that the transformation always creates a normal distribution.

By selecting a smaller alpha level a researcher is ___

reducing the risk of a type 1 error. The alpha level is the probability of a type 1 error. The smaller the alpha the smaller the probability

If a treatment has a very small effect, then a hypothesis test is likely to

result in a type 2 error

In a hypothesis test, the critical region consist of

sample values that are very unlikely to occur if the null hypothesis is true

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

slightly below the mean. The location is below the mean by 0.25 standard deviation

If other factors are held constant, the expected value of M will __ as the sample size increases

stay constant

What determines the probability of a type 1 error?

the probability is the alpha level selected by the researcher.