Data Analysis: Terms/HW/Practice (Exam 2)
Why are z-scores useful?
- gives us an understanding of where a score falls in relation to the mean of its underlying population - allows comparisons to be made between scores from different distributions - permits the transformation of z-scores into percentiles
A study of the Consideration of Future Consequences scale indicated a population mean of 3.20 and a standard deviation of 0.70. For a CFC score of 3.0, the z score would be? (round to the nearest 2 decimal places)
-0.29
The University of Minnesota graduate program in psychology has established a population mean GRE verbal score of 159, with a standard deviation of 2. A sample of 12 recently accepted students had a mean GRE verbal score of 157. Calculate the effect size (round to the nearest 2 decimal places):.
-1.00
Scores on the Wechsler Intelligence Scales for Children are standardized to have a mean of 100 and a standard deviation of 10. A sample of 99 students participated in an intervention meant to boost their scores on the test. The sample is found to have a mean of 102 Calculate the effect size.
0.20
After extensive measurements of the time necessary to complete the first homework assignment, a teacher determines that there is a population mean of 100 and a standard deviation of 20. If she samples a class of 43 students and calculates a mean of 101 minutes, what is the z statistic (round to the nearest 2 decimal places)
0.33
The average height of 15-year-old girls is 63.8 inches, with standard deviation of 2.66 inches. A teacher surveys her class of thirty-three 15-year-old girls and find average height of 62.6 inches What is the percentile rank for this sample? (rounded to the nearest 2 decimal places)
0.48
A standardized test has a population mean of 100 and a standard deviation of 20. Calculate that standard error for a sample of 500 students (round to the nearest 2 decimal places)
0.89
Previous research has found that college students have healthier eating habits, on average, than those who are neither college students nor college graduates. If the population mean for number of times eating breakfast per week is 4.5, with a standard deviation of 1, what is the approximate percentile for a student who eats breakfast 2 times per week? (whole number)
1
A standardized test has a population mean of 100 and a standard deviation of 20. Calculate the standard error for a sample of 45 students. (round to the nearest 2 decimal places)
2.98
A z-score of -1.0 is ___________ compared to a z-score of -2.0
higher
The practical use of statistical power is that it informs you the researcher:
how many participants are needed to conduct a study that will produce quality data that you can trust.
The statement "it is hypothesized that children who attend an enrichment program will score higher on IQ tests compared to children who do not attend enrichment program" best illustrates what?
one-tailed test
It becomes progressively easier to declare statistical significance as we increase:
sample size
The distribution of means has the same mean as the distribution of scores for the population, and the spread is:
smaller
Statistical power indicates
the likelihood of rejecting the null; if the null is false
The phrase statistically significant means that
the research result was unlikely to have occurred by chance
The formula for z based on the mean of a sample (as opposed to a single data point) is
z = (M - µM)/σM
Students were asked to rank their admiration of Jennifer Lopez and Venus Williams on a scale of 1-7. The population mean rating for Lopez was a 3.72, with a standard deviation of 1.90. The population mean rating for Williams was 4.58, with a standard deviation of 1.46. Another student Lynn, rated her admiration of Lopez at a 4 and Williams at a 5. Calculate Lynn's z score rating for both Lopez and Williams. What celebrity does Lynn admire most?
z score for Lopez: 0.15 z score for Williams: 0.29 Lynn admires Williams more
Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if their members have a different height, on average, from the population of American women. The mean height of group, which includes 25 members, is 65 inches. The z statistic for the sorority would be? The approximate percentile for this sorority would be?
z statistic : 2.50 approximate percentile: 99
A standardized test has a population mean of 250 and a standard deviation of 47. if a student earns a raw score of 391, her z score would be? (round to the nearest 2 decimal places):
3
Suppose that the known TV viewing habits for a certain state have a mean of 4.7 hours, with a standard deviation of 1.5 hours. A small farming town in the state believes that they have a different mean number of TV viewing hours. A sample of 82 people from this town is used and the mean of 3.9 viewing hours is obtained. Calculate an 80% CI
3.69, 4.11
A standardized test has a population mean of 250 and a standard deviation of 47. If a student earn a z score of 1.79, her raw score would be? (round to the nearest 2 decimal places)
334.13
Previous research has found that college students have healthier eating habits, on average, than those who are neither college students nor college graduates. If the population mean for number of times eating breakfast per week is 4.5, with a standard deviation of 1, what is the approximate percentage of students who eat breakfast between 4 and 5 times a week? (whole number)
34
Credit card companies will often call cardholders if the pattern of use indicates that the card might have been stolen. Let's say you charge an average $300 a month on your credit card, with a standard deviation of $50. The credit card company will call you anytime your purchase for the month exceed the 98th percentile. What is the dollar amount beyond which you'll get a call from your credit card company? (nearest whole number)
400
T/F If we know that the percentage of scores falling between the mean and a z score of 0.40 is 15.54, then the percentage of scores falling between the mean and a z score of -0.40 is 34.46?
False
T/F If we reject the null hypothesis, it means that the results of the study have practical importance
False
Cell phones are everywhere, and we are now available by phone almost all of the time. Does this translate into a change of the closeness of our long-distance relationships? What is the symbolic version of the null hypothesis?
Ho: μ(with_cellphones) = μ(without_cellphones)
A student wonders if grades in a class are in any way related to where a student sits in the classroom. In particular, do students who sit in the front row get better grades, on average, than the general population of students? What is the symbolic version of the null hypothesis?
Ho:μ(front_row_students) ≤μ(general_pop_students)
Under what conditions is it permissible to proceed with a hypothesis test even though the assumption that the population distribution is approximately normal is violated?
If we have a sample size that is greater than 30
With which p-level, 0.05 or 0.01, is it easiest to reject the null hypothesis, and why?
It is easier to reject the null hypothesis at the 0.05 level, because it has a larger critical region.
Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 10. A research study results in a 95% CI reported as (7.142, 9.865). What decision would you make based on this CI?
Reject the null hypothesis
In 1-2 sentences explain why the following statement is TRUE: It becomes progressively easier to declare statistical significance as we increase sample size.
This is true because when we increase our sample size, it will lower our standard error. (mean; z-tests) It basically makes it easier for us to reject the null: (statistically significant).
T/F A z test result is 4.12 would allow us to reject the null hypothesis, assuming we were conducting a two-tailed test with critical values of 1.96 and -1.96
True
By increasing statistical power, the probability of making a ________ error is __________.
Type II decreased
A new GRE prep class finds a sample from a recent session of their class has average scores that produce an effect size of d=2.6 compared to the known GRE average. Interpret the effect size.
We can interpret this effect size by saying that the GRE class had an average score of 2.6 standard deviation above the known GRE average.
If the cutoffs for a z test are -1.96 and 1.96, choose which of the following z scores would cause you to fail to reject the null hypothesis? (choose the appropriate scores) 2.5 -1.65 1.5 -1.99 0 1.76 -2.3
(anything in between the cutoffs) -1.65 1.5 0 1.76
If the cutoff for a one-tailed z test is -1.65, choose which of the following z scores would cause you to reject the null hypothesis (choose the appropriate scores) 0 1.5 2.5 -2.3 -1.96 -3.5 -1.2
(anything outside of the cutoff) -2.3 -1.96 -3.5
According to the ____________, as sample size increases, the distribution of _________ assume a normal shape
- central limit theorem - sample mean
We calculate a statistical power and find that it is 0.93. This means that if the null hypothesis is _____, we have a ________% chance of rejecting the null hypothesis.
false; 93
Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, often used to detect brain damage, starts with easy words like kangaroo and gets progressively more difficult, ending with words like sextant. The GNT population norm for adults in England is 20.4. Roberts (2003) wondered whether a sample of Canadian adults have different scores than adults in England. If they were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. Assume the standard deviation of adults in England is 3.2. 1.) If it is hypothesized that Canadians will have a lower mean, the researchers may choose to run a 1-tailed test (alpha = 0.05). For a one-tailed test, choose the appropriate null hypothesis. 2.) List the appropriate critical value for the 1-tailed test, using the correct sign (negative or positive). 3.) What conclusion do you draw from the hypothesis test, and why?
1.) Canadian adults do not have lower average GNT scores than English adults. 2.) -1.64, -1.65 (either or) 3.) Reject the null, since the test statistic value of z is in the critical region defined by the critical value.
Let's assume the average speed of a serve in men's tennis is around 135mph, with a standard deviation of 6.5mph. Because these statistics are calculated over many years and many players, we will treat them as population parameters. We develop a new training method that will increase arm strength, the force of the tennis swing, and the speed of the serve, we hope. We recruit 9 professional tennis played to use our method. After 6 months, we test the speed of their serves and compute an average 138mph. Calculate a 95% CI
133.75, 142.25
Most tests that give IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way in which people are categorized as having different levels of intellectual disability (the category formerly known as mental retardation). Prior to DSM-V, when the term mental retardation was used, four categories were distinguished. Two of those categories are shown below: -IQ of 20-35 (in combination with impaired life skills): severe mental retardation -IQ of 50-70 (in combination with impaired life skills): mild mental retardation People with scores above 70 were not considered to have mental retardation. The IQ test was used first, and then, if a person's score fell into the range for mental retardation (70 or below) above, that person would be assessed for life skill impairments. What percentage of people would be expected to have IQ scores that might put them into the mild mental retardation range? Assume that IQ scores are normally distributed in the population. (Enter a number without the percent sign, rounded to the nearest 2 decimal places)
2.26
A study of the Consideration of Future Consequences scale indicated a population mean of 3.20 and a standard deviation of 0.70. For a z score of -1.2, the raw score would be? (round to the nearest 2 decimal places)
2.36
Most tests that give IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way in which people are categorized as having different levels of intellectual disability (the category formerly known as mental retardation). Prior to DSM-V, when the term mental retardation was used, four categories were distinguished. Two of those categories are shown below: -IQ of 20-35 (in combination with impaired life skills): severe mental retardation -IQ of 50-70 (in combination with impaired life skills): mild mental retardation People with scores above 70 were not considered to have mental retardation. The IQ test was used first, and then, if a person's score fell into the range for mental retardation (70 or below) above, that person would be assessed for life skill impairments. A person falls at the 3rd percentile. What is his IQ score? (Enter a number only, rounded to the nearest 2 decimal places)
71.80
Imagine that your professor lost all records of students' raw scores on a recent test. However, she did record students' z scores for the test, as well as the class average of 41 out of 50 points and the standard deviation of 3 points (treat these as population parameters). She informs you that your z score is 1.10. What was your percentile score on this test? (rounded to the nearest 2 decimal places)
86.43
If the sorority actually had 9 members (still the same average height), would you expect the percentile value to increase or decrease (compared to you answer in the last question) Why?
Decrease because standard error of the sample average would increase with a smaller sample size
Suppose that for a particular study the expected value of a phenomenon is 0.00. The study results in a reported 95% CI of (-0.68, 0.11) What decision do you make based on the 95% CI?
Fail to reject the null because the population mean is within the CI
The population mean for certain aptitude test is known to be 35. To check the accuracy of this test, a random sample of individuals from the population is taken and then a 95% CI of (32.15, 36.89) is calculated. If a 99% CI were calculated based on the same data, it would ________ compared to the interval listed above.
be longer (include more values)
A behavioral neuroscientist is testing the effects of adrenaline on memory using a group of 12 rats. The researcher is unsure about how much adrenaline might produce an effect on memory. One group of rats will be injected with placebo saline (0 micrograms of adrenaline). The other group will be injected with a dose of adrenaline. When deciding between a 2-microgram dose or an 8-microgram dose (both of which are safe); the researcher opts to use the 8-microgram dose. The researcher has:
exaggerated the difference between the levels of her independent variable, thereby increasing her power.
An article in the journal Applied Nutritional Investigation reported the results of a comparison between a low-calorie soy-protein diet and a low-calorie traditional-protein diet. Twelve obese participants were randomly assigned to each diet. At the end of the diet period, those on the soy diet lost an average of 2.3% of their body fat. (SD= 0.55), while those on the traditional diet lost and average of 1.22% of their body fat (SD= 0.50). If we increase the sample size of this study, the value of the test statistic would ______ but the effect size would _______.
increase; remain the same
Imagine that a study of memory and aging finds that younger participants correctly recall 55% of studied words, older participants correctly recall 42% of studied words, and the size of this effect is Cohen's d = 1.5. According to Cohen's conventions for interpreting d, this effect is:
large
The larger the effect size, the:
less two distributions overlap
When Alpha increases, both (blank) and (blank) increase:
power; probability of a Type 1 error