Psych Stats Exam 2

Which of the following z-scores represent the location closest to the mean? a. -2.75 b. 1.20 c. - .25 d. .35

- .25

How to write a null hypothesis

H0=

A class consists of 30 males and 10 females. If the first randomly selected student was a female, what is the probability that the second randomly selected student will be a female as well?

.25 or 25%

If all scores in a population with µ = 100 and σ = 10 are transformed into z-scores, than the distribution of z-scores will have a mean of _____ and a standard deviation of _____.

0,1

IQ scores form a normal distribution with µ = 100 and σ = 10. Individuals with IQs above 130 are classified in the genius category. What proportion of the population consists of these individuals?

0.0013

A normal distribution has a mean of µ = 24 with σ = 2. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 20?

0.0228 or 2.28%

A normal distribution has a mean of μ = 32 and standard deviation of σ = 4. What is the probability of randomly selecting a score greater than 40 from this distribution?

0.0228 or 2.28%

A normal distribution has a mean of µ = 86 with σ = 6. What is the probability that the randomly selected score from this distribution will be less than X = 78?

0.0918 or 9.18%

What is the probability of randomly selecting a z-score greater than z = 0.5 from a normal distribution?

0.3085 or 30.85%

What proportion of a normal distribution is located between the mean and z = -1.00?

0.3413

What proportion of a normal distribution is located between the mean and z = 1.0?

0.3413

A class consists of 20 males and 30 females. What is the probability that a randomly selected student is a male?

0.40 or 40%

What is the probability of randomly selecting a z-score smaller than z = 0.75 from a normal distribution?

0.7734 or 77.34%

What is the probability of randomly selecting a z-score less than z = 1.75 from a normal distribution?

0.9599 or 95.99%

For a normal population with a mean of µ = 54 and a standard deviation of σ = 7, what is the probability of obtaining a random sample of n = 49 scores with the mean greater than M = 52?

0.9772 or 97.72%

A sample of n = 144 scores is randomly selected from a population with μ = 69 with σ = 12. On average, how much error is expected between the sample mean and the population mean, μ = 69?

1 point

A normal distribution of scores in population has a mean, µ = 94 and standard deviation, σ = 12. The distribution of sample means for samples of n = 16 that were randomly selected from this population will have an expected value of M equal ______ and a standard error equal _______.

94;3

Which of the following is a requirement for a random sample? A. Every individual must have an equal chance of being selected. B. The probabilities cannot change during a series of selections. C. There must be sampling with replacement.

ALL

how to write alternate hypothesis

H1=/

What decision should be made, if a hypothesis test produces a z-score in the critical region of the distribution of sample means?

Reject the null hypothesis.

What is measured by the numerator of the z-test statistic?

The actual difference between a sample mean M and the population mean µ.

Which of the following is an accurate description of the critical region for a one-tailed test?

The critical region is located only in one tail of the distribution.

When using a z-test for hypotheses testing, in what situation a research has the best chance to find a statistically significant effect of an experimental treatment?

When after the treatment, there is a large difference between the sample and population means, and the standard error is small.

A sample of n = 25 individuals is selected from a population with μ = 50 and σ = 10, and a treatment is administered to the sample. After treatment, the sample mean is M = 55. What is the Cohen's d effect size for this sample?

d = 0.50

In general, it is easier to reject a null hypothesis and conclude that the treatment produced a statistically significant effect when one uses a 2-tailed test instead of 1-tailed test.

false

For a population with a standard deviation of 8, what is the z-score corresponding to a score that is 4 points above the mean?

z =.5

For a population with µ = 56 and σ = 8, what is the z-score corresponding to X = 40?

z= -2

A sample of n = 20 scores has a mean of M = 25 and a standard deviation of s = 4. In this sample, what is the z-score corresponding to X = 30?

z= 1.25

fail to reject the null hypothesis

when you do not have enough statistical strength to show a difference or an association

reject the null hypothesis

when you have enough statistical strength to show a difference or an association

For a population with µ = 300 and σ = 20, what is the X value corresponding to z = 1.50?

x= 330

For a sample with M = 40 and s = 16, what is the X value corresponding to z = - 0.25?

x= 36

For a population with µ = 60 and σ = 8, what is the X value corresponding to z = - 2.00?

x= 44

For a population wit µ = 40 and σ = 4, what is the z-score corresponding to X = 46

z= 1.5

Which of the following z-scores correspond to a score that is above the mean by 3 standard deviations

z= 3

For a population with µ = 10 and σ = 4, what is the z-score corresponding to X = 12?

z=.50

For a population with µ = 10 and σ = 2, what is the X value corresponding to z = 2?

z=2

A researcher is conducting an experiment to evaluate the effectiveness of cognitive-behavioral therapy for eating disorder. The mean eating disorder score in clinical population of people suffering from the disorder is μ = 60. The results of the experiment will be examined using a z -test, two-tails. Which of the following is the correct statement of the null hypothesis, H0?

μ = 60 (i.e., the treatment has no effect).

A researcher is conducting an experiment to evaluate the effectiveness of treatment for depression in a population that is known to have a mean depression score of μ = 50. The results will be examined by a z-test, two-tails. Which of the following is the correct statement of the alternative hypothesis, H1?

μ ≠50 (i.e., the treatment has a significant effect).

A researcher administers a treatment to a sample of participants selected from a population with µ = 62. If the sample mean after the treatment is M = 70, which value of standard error,σM will result in the rejection of null hypothesis (assume p < 0.05, 2-tails test)?

σM = 4

A random sample of n = 64 scores is obtained from a population with a mean of µ = 130 and a standard deviation of σ = 20. If a sample is randomly selected from this population and the sample mean is M = 123, what is the z-score of the sample mean?

- 2.8

A sample is randomly selected from a population with μ = 100 and σ = 20. Which of the following samples would produce the most extreme z-score?

A sample of n = 100 scores with M = 105

What position in the distribution corresponds to a z-score of z = - 1.5?

Below the mean by a distance equal to 1.5 standard deviation

For an exam with a mean of M = 80 and a standard deviation of s = 6, Mary has a score of X = 88, Bob's score corresponds to z = +1.25, and Sue's score is located above the mean by 10 points. If the students are placed in order from lowest score to highest score, what is the correct order?

bob, mary, sue

In the adult population, the mean depression score is μ = 80 and σ = 18. A researcher wanted to investigate the effect of support groups on depression. She randomly selected a sample of n = 36 adults diagnosed with depression. The selected adults (i.e., the sample) attended a support group meeting every week for three months. Afterwards, the depression level of all participants was assessed and the mean depression score of the sample was M = 72. Do the data indicate a significant effect of attending support groups on depression? Use a two-tailed z - test with p < .05 to answer this research question.

- Null and alternative hypotheses - All computational steps of the z-test - Critical z-value used for decision about H0 - Decision about H0 (i.e., do you reject it or fail to reject it?) - If the effect is significant, compute the Cohen's d to establish the size of the effect - is the Cohen's effect small, medium or large? - Conclusion in APA reporting style

What proportion of a normal distribution is located in the tail beyond z = 1.0?

0.1587

A population has µ = 50. What value of standard deviation would make X = 45 a central (average) score in the population ?

10

A population has µ= 20. What value of standard deviation would make a score X = 25 an extreme value, out in the positive tail of the distribution?

2

A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .05. If the sample data produce a z-score of z = 1.87, what is the correct statistical decision and conclusion?

Fail to reject the null hypothesis and conclude that the treatment had no effect.

Under what circumstances will the distribution of sample means have a normal shape?

If the distribution of scores in the population is normal or the sample size is larger than 30.

A sample is randomly selected from a normal population with μ = 52 and σ = 10. Which of the following samples would be considered extreme and unrepresentative of this population?

M = 54 and n = 100

A researcher investigated the effect of physical exercise on self-reported stress level in a sample of n = 80 college students. The study outcomes were evaluated by the z - test, 2-tails & p < 0.5. If the sample data produce a z = -2.24, what is the correct decision about the null hypothesis and the conclusion from the study?

Reject the null hypothesis and conclude that there is a statistically significant effect of physical exercise on self-reported stress level.

Last week, Sarah had exams in English and in Biology. On the English exam, the mean was µ = 50 with σ = 5 and Sarah had a score of X = 55. On the Biology exam, the mean was µ=60 with σ = 10, and Sarah had a score of X = 70. In which class Sarah's performance was better based on this outcomes?

Sarah did equally well in both classes

The null and alternative hypotheses for z -test refer to which of the following?

The population after the treatment.

A researcher randomly selected a sample of n = 100 individuals from a population with µ = 75 and administer an experimental treatment to the sample. What the researcher should expect if the treatment has no effect?

The sample mean should be relatively close to 75 and should lead the researcher to fail to reject the null hypothesis.

A sample of n = 50 individuals is selected from a population with µ = 75, and a treatment is administered to the sample. What is expected if the treatment has a significant effect?

The sample mean should be very different from 75 and should lead you to reject the null hypothesis.

Which of the following accurately describes the sample means the critical region (i.e.,the rejection area) of the distribution of sample means for the z-test?

The sample means with a very low probability of being randomly selected from the population tested (i.e., the extreme sample means, relatively infrequent in the population tested).

What is indicated by the sign of a z score?

The sign of a z-score tells whether the score is located above (+) or below (-) the mean

What is measured by the denominator of the z-test statistic?

The standard error (i.e., the average difference between a sample mean M and the population mean µ that is expected if H0 is true).

A normal distribution has a mean of µ = 66 with σ = 8. What score separates the lowest 10% of the distribution from the rest of the scores? (Note: use the closest z value listed in the Unite Normal table).

X = 55.76

A distribution of exam scores is negatively skewed with M = 75 and s = 8. If these students' scores are transformed into z-scores, what is the shape of z-scores distribution?

negatively skewed

On an exam with M = 70, you have a score of X = 80. Which value of the standard deviation would give you the highest position in the class distribution?

s=5

distribution of sample means

the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population

what is indicated by the z score's numerical value?

the numerical value identifies the distance from the mean by measuring the number of standard deviations between the score and the mean.

standard error

the standard deviation of the distribution of sample means - measures variability