Part I

1. A researcher at The Downtown University has a set of data that contains the IQ scores for a sample of students in the university. The average IQ for the U.S. population of university students is 105.00. Make sure that you write down the appropriate formulas to answer the question(s).

1. Write the null and alternative hypotheses (symbols and words)
   H _o :
   H ₁ :

2. ---

   Identify the appropriate statistic(s) needed to answer this question and enter the formula(s) here
   See below
3. Find the mean, median, mode, range, interquartile range (IQR), and percentiles for the distribution
4. Calculate the sum of squares ( SS ), sample variance, sample standard deviation and the standard error of the mean for the dataset
5. Calculate a single sample t statistic to see if there is a statistically significant difference between the IQs of the students at Downtown U and the IQs of the average US university student (set alpha to = .05, two tails)
6. Graph the distribution using the appropriate graph(s) for the data
7. Could the sample the researcher has be considered to belong to the population? Yes No
8. Write up your conclusions about the sample means.

2. One sample has a mean of M = 4 and a second sample has a mean of M = 8. The two samples are combined into a single set of scores.

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. What is the mean for the combined set if both of the original samples have n = 7 scores?
3. What is the mean for the combined set if the first sample has n = 3 and the second sample has an n = 7?
4. What is the mean for the combined set if the first sample has n = 7 and the second sample has an n = 3?

3. The following frequency distribution summarizes the number of absences for each student in a class of n = 20:

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
   See below
2. Find the mode for this distribution
3. Find the median number of absences for this class
4. Explain why you cannot compute the mean number of absences using the data provided in the table

4. When the sun cannot be seen (overcast day), homing pigeons find their way back to their roosts by using magnetic cues from the earth (Walcott, 1972). Consider the following study. One sample of pigeons has a magnet fastened on their heads to interfere with their ability to detect the Earth’s magnetic field. A second sample has a nonmagnetic bar of equal size and weight placed on their heads. The pigeons are driven far from their roosts and then released. The researcher measures the error of the pigeons’ heading—that is, how many degrees there are between each pigeon’s course and the true course to the home roost. Hypothetical data are as follows:

1. Write the null and alternative hypotheses
   H _o :
   H ₁ :
2. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
   See below
3. Identify the independent and dependent variables
   Independent variable
   Dependent variable
4. Compute the means for the treatment groups
5. Compute the variance and standard deviation
6. Looking at the descriptive statistics, do you think that magnetic cues seem to help homing pigeons? Explain your answer

5. A distribution with a mean of = 86 and a standard deviation of σ = 12 is being transformed into a standardized distribution with = 100 and σ = 20.

Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here

See below

Find the new, standardized score (show work) for each of the following values:

1. X = 80
2. X = 89
3. X = 95
4. X = 98

6. Uptown University is planning some programs for various groups that will apply to the university. In order to complete the planning, the following information is needed from what is assumed to be normally distributed population. Assume that M = 500 and = 100.

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. What SAT scores ( X values) separate the middle 60% from the rest of the distribution?
3. What SAT scores ( X values) separate the middle 80% from the rest of the distribution?
4. What SAT scores ( X values) separate the middle 95% from the rest of the distribution?

7. One test for ESP involves using Zener cards. Each card shows one of five different symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is just guessing.

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. What is the probability of a correct prediction on any single trial?
3. What is the probability of correctly predicting exactly 20 cards in a series of n = 100 trials?
4. What is the probability of correctly predicting more than 30 cards in a series of n = 100 trials?

8. For a population with a standard deviation of σ = 20:

Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here

1. How large a sample would be needed to have a standard error less than 10 points?
2. How large a sample would be needed to have a standard error less than 4 points?
3. How large a sample would be needed to have a standard error less than 2 points?

9. Welsh, Davis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on a series of high-intensity exercises. One measure was how much time it took for the athletes to run to fatigue. Data similar to the results obtained are shown in the following table.

a. Construct a bar graph that incorporates all of the information in the table

b. Looking at your graph, do you think that the carbohydrate-electrolyte drink helps performance?

10. Assume that a treatment really does have an effect and that the treatment effect is being evaluated with a hypothesis test. If all other factors are held constant, how is the outcome of the hypothesis test influenced by sample size? To answer this question, do the following two tests and compare the results. For both tests, a sample is selected from a normal distribution with a mean of = 60 and a standard deviation of σ = 10. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 65. In each case, use a two-tailed test with = .05.

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. For the first test, assume the sample consists of n = 4 individuals.
3. Compute Cohen’s d for a sample of n = 4.
4. For the second test, assume the sample consists of n = 25 individuals.
5. Compute Cohen’s d for the sample of n = 25.
6. Explain how the outcome of the hypothesis test is influenced by sample size.
7. How is Cohen’s d influenced by sample size?

11. Researchers have often noted increases in violent crimes when it is very hot. In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball. That is, there is a much greater chance of a batter being hit by a pitch when the temperature increases. Consider the following hypothetical data. Suppose that over the past 30 years, during any given week of the major-league season, an average of = 12 players are hit by wild pitches. Assume the distribution is nearly normal with σ = 3. For a sample of n = 4 weeks in which the daily temperature was extremely hot, the weekly average of hit-by-pitch players was M = 15.5.

a. Write the null and alternative hypotheses

H _o :

H ₁ :

b. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here

c. Are players more likely to get hit by pitches during hot weeks? Set alpha to .05 for a one-tailed test (make sure you answer the question completely)

12. People tend to evaluate the quality of their lives relative to others around them. In a demonstration of this phenomenon, Frieswijk, Buunk, Steverink, and Slaets (2004) conducted fictitious interviews with frail elderly people. In the interview, each person was compared with others who were worse off. After the interviews, the elderly people reported more satisfaction with their own lives. Following are hypothetical data similar to those obtained in the research study. The scores are measures on a life-satisfaction scale for a sample of n = 9 elderly people who completed the interview. Assume that the average score on this scale is µ = 20. The life-satisfaction scores for the sample are 18, 23, 24, 22, 19, 27, 23, 26, 25.

a. Write the null and alternative hypotheses

H _o :

H ₁ :

b. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s)

c. Are the data sufficient to conclude that the people in this sample are significantly more satisfied than others in the general population? Use a one-tailed test with = .05. (Make sure you answer the question completely)

13. Coach Johnson believes that hockey players who wear helmets while playing hockey perform better in their classes than do those that do not wear helmets. Players were matched on IQ and high school grades and the pairs were assigned to groups. The Group 1 players wear helmets while playing and the Group 2 players do not. The player’s grade point averages were obtained as shown below.

1. Write the null and alternative hypotheses
   H _o :
   H ₁ :
2. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
3. Test the H _o ( = .05, two-tailed), compute the estimated d (effect size), and compute the percentage of variance explained ( r ² ) for the sample of hockey players
4. Write up your conclusions about the differences

14. A common test of short-term memory requires participants to repeat a random string of digits that was presented a few seconds earlier. The number of digits is increased on each trial until the person begins to make mistakes. The longest string that can be reported accurately determines the participant’s score. The following data were obtained from a sample of n = 9 participants. The scores are 4, 3, 12, 5, 7, 8, 10, 5, 9.

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. Compute the mean and variance for the sample
3. Use the data to make a point estimate of the population mean
4. Construct an 80% confidence interval estimate of µ (two-tails)

15. A psychologist is interested in examining how the rate of presentation affects people’s ability to memorize a list of words. A list of 20 words is prepared. For one group of participants the list is presented at the rate of one word every ½ second. The next group gets one word every second. The third group has one word every 2 seconds, and the fourth group has one word every 3 seconds. After the list is presented, the psychologist asks each person to recall the entire list, the dependent variable is the number of errors in recall. The data for this experiment are as follows:

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. Can the psychologist conclude that the rate of presentation has a significant effect on memory? Test at the .05 level
3. Create a source table to display your findings
4. Use the Tukey HSD to determine which rates of presentation are statistically different and which ones are not
5. Explain your findings based on the post hoc tests. Make sure you fully explain your findings and show your work

16. To test the effectiveness of a new studying strategy, a psychologist randomly divides a sample of 10 students into two groups, with n = 5 in each group. The students in one group receive training in the new studying strategy. Then all students are given 30 minutes to study a chapter from a history textbook before they take a quiz on the chapter. The quiz scores for the two groups are as follows:

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. Convert these data into a form suitable for the point-biserial correlation. (Use X = 1 for training, X = 0 for no training, and the quiz score for Y )
3. Calculate the point-biserial for these data
4. Discuss your findings—is there a relationship between training strategy and the quiz scores?

17. For the data, below:

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. Compute the regression equation for the data in the table, below (show all work)
3. Create the appropriate graph for these data and plot the regression line for the computed regression equation

18. A professor in the psychology department would like to determine whether there has been a significant change in the grading practices over the years. It is known that the overall grade distribution for the department in 2000 had 14% As, 26% Bs, 31% Cs, 19% Ds, and 10% Fs. A sample of 200 psychology students from last semester produced the following grade distribution:

1. Identify the appropriate statistic(s) needed to answer this question and enter the formula(s), here
2. Write the null and alternative hypotheses
   H ₀ :
   H ₁ :
3. Has there been a change in grading practices? Explain your findings and show your work.

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