PSYCH 2220 exam 1
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 of $300 a month on your credit card, with a standard deviation of $50. The credit card company will call you anytime your purchases for the month exceed the 98th percentile. What is the dollar amount beyond which you'll get a call from your credit card company? (Enter the dollar amount rounded to two decimal places)
$402.50
List the appropriate critical value for the 1-tailed test, using the correct sign (negative or positive).
-1.64 -1.65
If the critical values 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. (select the appropriate z score or scores)
-1.65 1.5 0 1.76
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 (round to the nearest 2 decimal places):
.20
A researcher is conducting eye-tracking research. In a 5-second period, she measures an average of 15 saccades (eye movements), with a standard deviation of 2. If 50 people participated in the study, about how many participants had between 13 and 17 saccades in the 5-second period (assuming normality of the data)?
.34
A student gathers data on math anxiety. Of her participants, 45 had no math anxiety and 60 experienced math anxiety within the past month. What is the probability of selecting a participant who experiences math anxiety based on this data set? Report your answer rounded to the nearest 2 decimal places.
.57
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 percentile for a student who eats breakfast 2 times per week? (List your answer IN PERCENT FORM to 1 decimal place)
.6
Students were asked to rank their admiration of Jennifer Lopez and Venus Williams on a scale of 1 (low) to 7 (high). 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, Jasjit, rated her admiration of Lopez at a 5 and Williams at a 6. Calculate Jasjit's z score for her rating of Lopez (round to the nearest 2 decimal places). Calculate Jasjit's z score for her rating of Williams (round to the nearest 2 decimal places). Compared to the other students in this database, which celebrity does Jasjit most admire (based on the z scores above)? Enter either "Lopez" or "Williams" as your answer.
.67 .97 Williams
Some cognitive neuroscience researchers were interested in the stability of Blood-Oxygenated Level Dependent (BOLD) signal changes in supplementary motor areas (SMA) of the brain during a motor task performed in a functional imaging experiment. For this exercise suppose the researchers have so much data that their findings represent population parameters. The researchers found that signal change of the SMA has mean of 1.10 and standard deviation of 0.80. On another day they resampled 25 participants and found the group had a mean signal change of 1.29. To understand if this resampled group would be representative, calculate a 95% confidence interval. List the lower bound (rounded to 2 decimal places): and the upper bound (rounded to 2 decimal places):
.98 1.60
A standardized test has a population mean of 100 and a standard deviation of 20. Calculate the standard error for a sample of 500 students (round to the nearest 2 decimal places).
0.89
If the critical value for a one-tailed z test is -1.65, choose which of the following z scores would cause you to fail to reject the null hypothesis. (select the appropriate z score or scores)
1.5 0 -1.2 2.5
For a set of 6 numbers, sample standard deviation = 11. For this data, sample variance = (enter as a whole number with no decimals)
121
Suppose that the known TV viewing habits for a certain state have a mean of 4.7 hours, with a standard deviation of 1.3 hours. A small farming town in the state believes that they have a different mean number of TV viewing hours. A sample of 78 people from this town is used and the mean of 4.1 viewing hours is obtained. Calculate an 80% confidence interval. List the lower bound (rounded to 2 decimal places): and the upper bound (rounded to 2 decimal places):
3.91 4.29
An instructor was interested in the variability of her entire class's exam scores and collected the following data. 92, 86, 72, 83, 95, 82, 85, 88 Identify the correct formula for the population variance.
339.875/8
Based on the following set of data: X = {36, 101, 55, 40, 37, 42, 43, 110}, first calculate Q1: Next, calculate Q3: Finally, calculate the interquartile range:
38.5 78 39.5
As a measure of variability, calculate the sample standard deviation for the following set of data: x = {110, 36, 55, 40, 37, 42, 43, 101} Report the sum of squares used in the sample standard deviation formula. *Keep your work out to 3 decimal places and round your final answer to 2 decimal places (ex: round 1.7896 to 1.79).
6,292
An instructor was interested in the variability of her class's attendance and collected the following data for all student's in her class. 38, 45, 44, 30, 42, 17, 41, 44, 40 Identify the appropriate denominator for the population standard deviation calculation.
9
Daily low temperatures in Columbus, OH in January 2014 were approximately normally distributed with a mean of 15.45 degrees and a standard deviation of 13.70. What percentage of days had a low temperature between 5 degrees and 9 degrees? (List your answer to 1 decimal place.) *Use z Converter
9.5%
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.
Canadian adults do not have lower average GNT scores than English adults.
A researcher compared the height of 2-year-old children and 5-year-old children. Height in inches is what type of variable?
Continuous
An instructor planned to analyze the number of missed assignments for each student in her class. The number of missed assignments is what type of variable?
Discrete
sum of squares formula
E(X-M)^2
Suppose that for a particular study the expected value of a phenomenon is 0.00. The study results in a reported 95% confidence interval of [-0.68, 0.11]. What decision do you make based on the 95% confidence interval?
Fail to reject the null because the population mean is within the confidence interval.
If we reject the null hypothesis, it means that the results of the study have practical importance.
False
How do we know that the probability of flipping heads with a fair coin is 50%?
Heads is one outcome out of 2 possible outcomes, which equals a probability of 50%.
How do histograms differ from bar graphs?
Histograms are typically used to depict scale data, but bar graphs are typically used to depict nominal or ordinal data.
For the following example, select the symbolic version of the two-tailed null hypothesis. A researcher is interested in studying the relation between the use of antibacterial products and the dryness of people's skin. He thinks these products might alter the moisture in skin differently from other products that are not antibacterial.
Ho: μ(antibac) = μ(non-antibac)
For the following example, select the symbolic version of the one-tailed null hypothesis: 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?
Ho: μ(front_row_students) ≤ μ(general_pop_students)
Assume a researcher wants to understand usage pattern of buses in Columbus. She passes out a survey on the bus where one question is "Which bus route do you use most often?". The following subset of a larger data set is X = {10, 11, 2, 8, 21, 2, 2, 8, 18, 14, 10}. (NOTE: each number corresponds to a bus route)
IQR, SD,range,variance,None of the above
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.
A group of undergraduate students are exploring starting salary for several jobs of interest. The students are aware that for each job they are examining, there are a few individuals who earn much more than others due to past work experience. Which measure of central tendency should they compare for the starting salary of the various jobs?
Median, because it is more representative of the middle range of starting salary values.
In a student survey, researchers recorded preferred class format (online or in-person), current GPA, hours of sleep per night, and major. When analyzing preferred class format, which measure of central tendency would be appropriate?
Mode, to express the most common response.
nominal
Nominal, which means "in name only," is a measurement with unordered categories that are names, types, or labels. A variable's level of measurement, such as the nominal level, influences the choice of statistics by the kinds of mathematical operations that can be performed with the variable. The only mathematical operations that are possible with nominal-level measurements are equality or inequality. We can say that two observations are unequal on the social media measurement if one observation is Instagram and another is TikTok. Looking at a whole data set, we can count how many observations in the sample were Instagram and how many were TikTok, Snapchat, etc., but we cannot order the responses in any meaningful way.
An instructor could use the mean to represent the central tendency of which of the following variables?
Points earned on an exam
An instructor wanted to compare average hours of sleep between their morning and afternoon classes. How would you classify hours of sleep?
Quantitative variable
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% confidence interval reported as [7.142, 9.865]. What decision would you make based on this confidence interval?
Reject the null hypothesis.
What conclusion do you draw from the hypothesis test, and why?
Reject the null, since the test-statistic value of z is in the critical region defined by the critical value.
A researcher is studying anxiety. The first sample she collects (n = 25) has a mean of 4.5 on an anxiety scale. The second sample (n = 46) has a mean of 4.7 on the same anxiety scale. Which sampling distribution likely has less variability?
Study 2, n = 46
A research team conducts a study on stress levels after a workout. The results of the hypothesis test provide a p-value of .06. Choose the correct interpretation of this p-value.
The probability of observing the calculated test statistic (or one that is more extreme), assuming the null distribution is true, is 6%.
A sample of 14 quiz scores had a variance 0.81 and a standard deviation of 0.90. Why might a researcher choose to report the standard deviation and not the variance?
The standard deviation is interpreted in the units of the scores recorded.
A researcher recorded time to complete standardized assessments. The researcher found that the minutes to complete standardized test A had a population variance of 31.45 and the minutes to complete standardized test B had a population variance of 45.32. Assume both populations are normally distributed.
There is more variability in the scores for test B compared to test A.
Musab is interested in determining if people who eat breakfast in the morning are more energized at the end of the day than people who do not eat breakfast. In his sample, he finds that there is no difference in energy levels at the end of the day between these two groups. If breakfast eaters actually are more energized than those who do not eat breakfast, what type of error did Musab make?
Type II error
Identify the scenario when a frequency polygon would be more useful than a histogram.
When comparing the number of students who attended 0 to 30 classes over the semester, and separating out freshman, sophomores, junior, and seniors.
How do you know for certain if you made a Type I or Type II error in a research study?
You cannot know for certain if you made a statistical error.
Why would you want to limit sampling error?
You want the sample to be as representative of the population as possible.
Anxiety scores from a sample of 150 participants were approximately normally distributed, with a large standard deviation. In a frequency distribution, you would expect to see
a low peak, with few scores clustered around the mean.
A researcher wanted to determine whether eating Pop-Tarts for breakfast increased the aggression of second graders during their morning play period. After feeding a group of 20 2nd grade students Pop-Tarts for breakfast she observed that, on average, the students committed 4.5 aggressive behaviors during their morning play period. In this example, the population is:
all second graders who eat Pop-Tarts for breakfast.
ratio
atio scale of measurement is one that, in addition to having ordered, equally-sized increments, does have a true, meaningful zero point. As a result, on a ratio-level scale, it is meaningful to compare ratios of values. When measuring time, such as minutes spent on social media today, 0 minutes is meaningful as it indicates the absence of time, even if the value 0 is not part of your data. In addition, ratios are an appropriate comparison of minutes: 60 minutes spent on social media is twice as much as 30 minutes. Other examples of ratio measurements are income in dollars, weight in pounds or kilograms, years of age, and reaction time.
Sun is reading an article about autism rates and how they are increasing in a majority of Western countries around the world. She notices that the authors used a _____ to depict the number of autism diagnoses in five different countries. This is the appropriate graph because the variables are _____.
bar graph; nominal and scale.
An instructor compared average final course grade for biology majors, psychology majors, economics majors, and education majors. What type of graph should the instructor use to illustrate his findings and why is that graph appropriate?
bar graph; there is 1 nominal variable and 1 scale variable
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% confidence interval of [32.15, 36.89] is calculated. If a 99% confidence interval were calculated based on the same data, it would _____ compared to the interval listed above.
be longer (include more values)
Wendy is a Weight Watchers group leader. To get a better idea of how to help those she will be working with to achieve their weight-loss goals, she wishes to know the average weight-loss goal of the individuals in her group. What kind of statistic should Wendy use?
descriptive
The United States Department of Homeland Security Threat Advisory System measures threat as severe, high, elevated, guarded, or low. In this system, threat is a ________ variable.
discrete and ordinal
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.
The statement "There was no significant relationship between anxiety and food consumption in the current study" indicates that the researcher should ________ hypothesis.
fail to reject the null
We calculate a statistical power and find that it is 0.65. This means that if the null hypothesis is ________, we have a ________% chance of rejecting the null hypothesis.
false; 65
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.
To test whether a chemical found in many common plastic items is toxic, researchers fed different amounts of the chemical (from 0 to 20 micrograms) to mice and later performed a blood test to determine the amount of toxins present in each mouse. To create a scatterplot of the data, which variable should be listed on the x-axis?
independent variable, which is the amount of the chemical given to the mice
interval
interval scale of measurement has mutually exclusive, ordered, equal-sized increments, without a meaningful 0. The distance from 2019 to 2020 is one year, just as the distance from 2020 to 2021 is one year, and the years can be placed in a meaningful order; year 0, however, does not signify an absence of time. The absence of an absolute 0 is reinforced as calendars can differ in the placement of year 0. Notice that the interval scale allows for a comparison of differences along the scale (again, if you move 1 year, then you move the same distance no matter where on the scale you start), but it does not allow for comparisons of ratios (e.g., the year 500 is not ¼ the size of the year 2000, but it is 1500 hundred years earlier). A common example of an interval scale of measurement is temperature measured in degrees Fahrenheit or Celsius.
The range as a measure of variability is problematic because:
it relies on the most extreme scores which could be outliers.
Reaction times were normally distributed in a sample of 254 measurements. The next two participants took much longer to complete the task and their scores were outliers. The addition of these 2 scores would influence which measure(s) of central tendency?
mean
A researcher was interested in assessing whether a new medication had negative side affects on reaction time. He performed an experiment on a group of rats. One group of rats received the medication, and the other group of rats did not. The researcher then measured reaction time differences between the two groups on a series of tasks. In this experiment, the independent variable is:
medication
Assume a researcher wants to understand usage pattern of buses in Columbus. She passes out a survey on the bus where one question is "Which bus route do you use most often?". The following subset of a larger data set is X = {10, 11, 2, 8, 21, 2, 2, 8, 18, 14, 10}. (NOTE: each number corresponds to a bus route) Pick all measures of central tendency that are appropriate for this data (select one or more):
mode
A health psychologist studies food intake by recording the type of food consumed by participants at lunch (such as: meat, carbohydrate, vegetable, dairy). The scale of measurement for type of food would be:
nominal
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 an enrichment program" best illustrates a:
one-tailed hypothesis.
There are three different types of Olympic medals: gold, silver, and bronze, which represent the final rank at which a competitor completes his/her event. What kind of variable describes the different types of Olympic medals?
ordinal
ordinal
ordinal scale of measurement indicates that a measurement is ordered on an underlying dimension, but there is not equal spacing between each unit of measurement. As we rank our preference of social media platforms, the values might be 1st (favorite), 2nd, 3rd, and so on, until we reach our least favorite. There is a clear order in terms of preference, but the spacing along the continuum is not necessarily equal. The step between 1st and 2nd might not be the same as the step between 3rd and 4th. This means we cannot add and subtract the values on an ordinal scale, even though the values are often expressed with numbers. Ordinal values can be compared as equal or unequal and greater than or less than (e.g., the social media rankings can be compared as more or less preferred).
A graduate statistics class is unhappy with the midterm grades. The majority of students scored 45 or below on a 100-point scale, with just several students performing very well. Which type of distribution do the test scores represent?
positively skewed
For a set of 50 numbers a researcher calculates the following measures of central tendency: mode = 5, median = 40, mean = 60. This distribution of this data would be considered:
positively skewed
When alpha increases, both ________ and ________ increase.
power; probability of a Type I error
A researcher recorded the length of REM for participants in a sleep study. To understand the spread of the data from the least time in REM to the most time in REP should should calculate the
range
It becomes progressively easier to declare statistical significance as we increase:
sample size.
A researcher investigated the relationship between IQ score and years of education (measured as 1-16). What type of graph should the researcher use to illustrate his findings?
scatterplot because it will show the relationship
A research team analyzed data from 45 college students on the number of number of social media apps on their smartphone. The mean number of social media apps for these 45 students would be considered a
statistic
According to ________, as sample size increases, the distribution of ________ assume a normal shape.
the central limit theorem; sample means
Which of the following has the greatest probability of occurring?
z-score between 0 and 0.5
The mean of the population is represented by the symbol ________ and the mean of the sample is represented by the symbol ________.
μ; M
Variance formula
∑(x - X)²/n-1