Stats Final 5-8
A researcher conducts a Z-test comparing a sample Mean (20) to a population Mean of (25) and a SD of (2). He obtains a Z score of 2.3, which is statistically significant. Calculate the effect size for this score (Cohen's d).
-2.5
A researcher selects a sample of size 6 from a population of size 10. How many possible samples of this size can be selected using theoretical sampling?
1,000,000
Based on the effect size conventions, d = 0.18 is a
small effect size
Increasing sample size will
Increase the power of the decision.
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
A researcher is interested in studying whether or not listening to music while jogging makes people run faster. He thinks that listening to music will make people run faster. Luckily, he knows that, for the population he interested in (runners in Washington, DC), the mean running speed (μ) is 6mph, and the standard error is 2mph. He collects data from a sample of runners that only listen to music, and finds they have a mean running speed (M) of 9mph. State the hypothesis H0: H1:
Selected Answer: H0: mean is equal to 6mph. Listening to music does not make people run faster. H1: mean is greater than 6mph. Listening to music makes people run faster. Correct Answer: H0: M ≤ 6 H1: M > 6
A researcher determines that the probability of winning a new game is p = .32. Assuming winning and losing are mutually exclusive events, what is the probability of winning and losing the new game?
This outcome is not possible.
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.
What is the z score for scores in the bottom 5%?
-1.645
Calculate the corresponding X value for a Z-score of 1.21 from a distribution with a Mean of 125 and a SD of 30
161.3
An articles states that a sample of 40 participants took 12 ± 2.3 ( M ± SEM) seconds to complete a cognitive assessment. Which value is the standard error of the mean?
2.3
Which of the following is not a step to locate a proportion in a normal distribution?
Convert a proportion to a standard normal z score.
Calculate the probability of getting a score higher than 102 from a distribution with a Mean of 82 and a SD of 9
Correct answer: 0.0132 Answer range: +/- 0.001 (0.0122 - 0.0142)
In a normal distribution a score of 8 will always be more probable than a score of 0.
False
The probability of an outcome is particularly useful for predicting the likelihood of fixed events
False
The standard deviation and the mean can equal 0 in a data set that is normally distributed.
False
Which of the following is not one of the four steps to hypothesis testing?
evaluate the plan
Based on the effect size conventions, d = 0.60 is a
medium effect size
Calculate the a Z-score for X=14, from a distribution with a Mean of 49 and a SD of 12.
-2.916
Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16. Assuming independent outcomes, the probability that two children of alcoholic parents will be alcoholic equals
.03
A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and 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 population.
A marketing researcher is interested in the number of songs that millenials include on their playlists. He collects data from a sample of millenials and finds the following frequency distribution: Number of songs. Proportion 10 0.1 15 0.14 20 0.15 25 0.11 30 0.13 35 0.16 40 0.09 45 0.07 50 0.05 What is the standard deviation of the number of songs from this sample? (the SD of the probability distribution)
Selected Answer: 11.74 Correct Answer: 11.5 Answer range +/- 5 (6.5 - 16.5)
The z score cutoff for the top 50 percent of scores in any normal distribution is 0.
True
There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1.
True
All z scores above the mean are positive, whereas all z scores below the mean are negative.
True
An example of a binomial variable includes
sex (male, female)
A researcher is interested in studying whether or not listening to music while jogging makes people run faster. He thinks that listening to music will make people run faster. Luckily, he knows that, for the population he interested in (runners in Washington, DC), the mean running speed (μ) is 6mph, and the standard deviation is 2mph. He collects data from a sample of runners that only listen to music, and finds they have a mean running speed (M) of 9mph. The researcher would like to conduct a One-Sample Z-test. Please calculate the Z-statistic (Z-obtained)
1.5
A marketing researcher is interested in the number of songs that millenials include on their playlists. He collects data from a sample of millenials and finds the following frequency distribution: Number of songs. Proportion 10 0.1 15 0.14 20 0.15 25 0.11 30 0.13 35 0.16 40 0.09 45 0.07 50 0.05 What is the average expected number of songs from this sample? (the mean of the probability distribution)
27.6
A researcher determines that the probability of missing class among students at a local school is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution.
48 students
A researcher is interested in constructing a sampling distribution for a population of values. She settles on a sample size of n=4, from a population of N=50. How many possible combinations could she obtain if she were sampling with replacement?
6250000
A researcher is studying a small population (N=8). He decides to sample without replacement, for a sample size of n=4. How many possible combinations could he obtain?
70
A researcher records the following data for the number of bids made on a sample of items sold at an auction. Based on the table, what was the probability that an item had 7 bids made on it? Number of Bids Frequencies 3 5 4 12 5 7 6 6 7 10
.25
A researcher records the number of job openings among small businesses. She finds that the probability that a small business has 0 job openings is p = .22; 1 job opening is p = .45; 2 job openings is p = .08; and 3 job openings is p = .25. What is the probability that a small business has at least 2 job openings?
.33
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
The ________ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1.
standard normal transformation
What is the z score for scores in the top 2.5%?
1.96
A theoretical distribution that evenly distributes data around the mean, median, and mode is called the
all of the above
Because the sampling distribution of sample means is normally distributed, we can use the z transformation formula to find probabilities. Which of the following gives the appropriate notation for this formula?
all of the above
The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n - 1)
are both unbiased estimators
A researcher selects a sample of 16 participants from a population with a variance of 4. What is the standard error of the mean?
less than 1
In terms of estimating the population variance, what is one disadvantage for dividing SS by df to calculate sample variance?
It does not have minimum variance.
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.
Complementary outcomes are exhaustive of all possible outcomes.
True
Probability ranges between 0 and 1 and is never negative.
True
The multiplicative rule is used for independent outcomes
True
The probability of correctly rejecting a false null hypothesis is called the power of the decision-making process.
True
The sample mean is an unbiased estimator of the population mean.
True
The typical level of significance in hypothesis testing in the behavioral sciences is set at .05.
True
The value of power is influenced by the alpha level, sample size, and effect size.
True
The probability of a college student being employed is p = .35. The probability of a student being employed and dropping out of college is p = .20. Hence, the probability of a student dropping out of college, given that he or she is employed, is
p = .57
