You are a researcher who wants to know if there is a relationship between variable Y and variable X. You hypothesize that there will be a strong positive relationship between variable Y GPA and Variable X hours of sleep. After one semester, you select five students at random out of 200 students who have taken a survey and found that they do not get more than 5 hours of sleep per night. You select five more students at random from the same survey that indicates students getting at least seven hours of sleep per night. You want to see if there is a relationship between GPA and hours of sleep. Using a Pearson Product Correlation Coefficient statistic, determine the strength and direction of the relationship and determine if you can reject or fail to reject the HO:

Variable Y        Variable X    

2.5                      5               

3.4                      8                

2.0                      4               

2.3                     4.5              

1.6                     3     

3.2                     6

2.8                     7

3.5                     7.5

4.0                     6.5

3.8                     7

Generally, the average typing speed is 56 words per minute (wp). A professor wanted to see where his students stand compared to the population. He tested 30 of his students and obtained the following estimates: an average typing speed of 49 with a standard deviation of 16. What can the professor conclude with α = 0.01?

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- the students student typing speed average typing speed typing speed the professor
Sample:
---Select--- the students student typing speed average typing speed typing speed the professor

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

11) You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats.
You sample 180 men, and 30% own cats.
You sample 100 women, and 70% own cats.
Find the test statistic, rounded to two decimal places.

12) You are testing the claim that the mean GPA of night students is different than the mean GPA of day students.
You sample 60 night students, and the sample mean GPA is 2.01 with a standard deviation of 0.53
You sample 30 day students, and the sample mean GPA is 1.75 with a standard deviation of 0.74
Calculate the test statistic, rounded to 2 decimal places

20) Give a 98% confidence interval, for μ1-μ2 given the following information.

n1=35, ¯x1=2.69, s1=0.47
n2=25, ¯x¯2=2.42, s2=0.99

___ < μ1-μ2 < ___ Use Technology Rounded to 2 decimal places.

Answer the questions below using the appropriate statistical technique. For questions involving the use of hypothesis testing, you must:

1. State the null and research hypotheses

2. Provide the Z(critical), T(critical), or χ 2 (critical) score corresponding to the α threshold for your test

3. Provide your test statistic

4. Provide your decision about statistical significance

An advantage that often comes with a basic knowledge of statistics is a change in salary. To see whether this was the case for Tulane University graduates, you took a random sample of 57 students who completed a statistics class and asked about their starting salaries (in thousands) after graduation. The sample had a mean of 53.3 with a standard deviation of 3.72 (i.e., x = 53.3 and s = 3.72). A call to the Office of the Registrar indicates that the average starting salary value for all Tulane students is 47.1. Do students who take statistics courses earn an equal salary compared to Tulane students generally? Use α = 0.001.

A newspaper article reported that a computer company has unveiled a new tablet computer marketed specifically to school districts for use by students. The new tablets will have faster processors and a cheaper price point in an effort to take market share away from a competing company in public school districts. Suppose that the following data represent the percentages of students currently using the company's tablets for a sample of 18 U.S. public school districts. (Round your answers to two decimal places.)

13 20 10 19 24 16 40 27 62 18 13 20 16 22 25 22 24 17

(a) Compute the mean and median percentage of students currently using the company's tablets. mean % ___median % ___

(b) Compute the first and third quartiles (as percentages) for these data. Q1 % ___ Q3 % ____

(c) Compute the range and interquartile range (as percentages) for these data. range %____ interquartile range %____

(d) Compute the variance and standard deviation (as a percentage) for these data. variance ____standard deviation % ____

(e) Are there any outliers in these data? There____ below the lower limit and _____above the upper limit.

(f) Based on your calculated values, what can we say about the percentage of students using the company's tablets in public school districts?

a. Use of the tablets is very low for all school districts.

b.Use of the tablets is very high for all school districts.

c. Relative to the mean, there are some school districts where many more students are using the tablets.

d.Relative to the mean, there are some school districts where much fewer students are using the tablets.

e.Relative to the mean, use of the tablets is similar for all school districts.

7. Problems and Applications Q7

Three students have each saved $1,000. Each has an investment opportunity in which he or she can invest up to $2,000. Here are the rates of return on the students’ investment projects:

Assume borrowing and lending is prohibited, so each student uses only personal saving to finance his or her own investment project.

Complete the following table with how much each student will have a year later when the project pays its return.

Now suppose their school opens up a market for loanable funds in which students can borrow and lend among themselves at an interest rate rr.

A student would choose to be a borrower in this market if his or her expected rate of return is than rr.

Suppose the interest rate is 6 percent.

Among these three students, the quantity of loanable funds supplied would be, and quantity demanded would be.

Now suppose the interest rate is 12 percent.

Among these three students, the quantity of loanable funds supplied would be, and quantity demanded would be.

At an interest rate of, the loanable funds market among these three students would be in equilibrium. At this interest rate, would want to borrow, and would want to lend.

Suppose the interest rate is at the equilibrium rate.

Complete the following table with how much each student will have a year later after the investment projects pay their return and loans have been repaid.

True or False: Both borrowers and lenders are made better off.

True

False

A study by Staub, 1970, was concerned with the effects of instructions to young children and their subsequent attempts to help another child (apparently) in distress. Twenty-four first-grade students were randomly assigned to one of three groups. The first group was labeled as indirect responsibility (IR). Students in the IR group were informed that another child was alone in an adjoining room and had been warned not to climb up on a chair. The second group was labeled direct responsibility one (DR1). Students in the DR1 group were told the same story as in the IR condition, but was also told that they were left in charge and to take care of anything that happened. The students were given a simple task, and the researcher left the room. The students then heard a loud crash in the adjoining room followed by a minute of sobbing and crying. Students in the third group, direct responsibility two (DR2), had the same instructions as the DR1 group, but the sounds of distress also included calls for help. Ratings from 1 (no help) to 5 (went to the adjoining room) were given to each student by an observer sitting behind a one-way mirror. The ratings are given below.

PART A: Perform a one-way ANOVA in SPSS with α = .05

PART B: Write an APA-style summary of your findings for the study based on the analyses you just completed (No more than half a page - no less than 2 paragraphs).

Suppose you are looking at the population of 8,000 students that are freshman at UTEP. You want to determine on average how many hours a week they work each week. Let’s call that number ?. You decide to take a sample of 100 of them.

• 1) How many data points are there in this space?
• 2) How many ways can you choose your subest of 100 students? Is it greater or less than the answer above.
• 3) How do you calculate the “point estimate” of one of those subsets of 100 students?
• 4) How many actual subsets of 100 students do you have as a researcher?
• 5) What does the Central Limit Theorem say about all the possible point estimates that can occur from the possible 100-student subsets? Draw a graph.
• 6) What value is the center of that curve? Please label it on the graph above.

Let’s just say the standard deviation of those 8,000 students is 5.

• 1) What is the formula for standard deviation of a population the 8,000 students (please make sure the summation sign has a starting and ending number)? Can it ever be negative? In our example, what are the units of the standard deviation?
• 2) What does the Central Limit Theorem say about the standard deviation of the curve discussed in question 5) above?
• 3) What is the standard deviation in our example?
• 4) What is the probability that a randomly picked sample has a point estimate within .5 of
  the actual mean ??
• 5) What is the probability that a randomly picked sample has a point estimate within 1 of
  the actual mean ??
• 6) Do you know whether our point estimate is higher or lower than the mean?

You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. A sample of 22 night students and 25 day students and their GPA's are recorded below. Test the claim using a 5% level of significance. Assume the population variances are unequal and that GPAs are normally distributed. Give answers to 4 decimal places.

What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem.

H₀: ______ s² σ² μ₁ μ₂ x̅₁ x̅₂ p [ > ≠ ≥ < = ≤ ] _______μ₂ s² p x̅₂ x̅₁ μ₁ σ² 0

H₁: ________ x̅₁ s² μ₁ x̅₂ μ₂ σ² p [≥ ≤ > = ≠ <] ________s² 0 μ₁ σ² x̅₂ p x̅₁ μ₂

Based on the hypotheses, find the following:

Test Statistic=

p-value=

The correct decision is to Select an answer reject the claim reject the null hypothesis fail to reject the null hypothesis accept the null hypothesis accept the alternative hypothesis  .

The correct summary would be: Select an answer There is not enough evidence to support the claim There is enough evidence to reject the claim There is not enough evidence to reject the claim There is enough evidence to support the claim  that the mean GPA of night students is different from the mean GPA of day students.

A study by Staub, 1970, was concerned with the effects of instructions to young children and their subsequent attempts to help another child (apparently) in distress. Twenty-four first-grade students were randomly assigned to one of three groups. The first group was labeled as indirect responsibility (IR). Students in the IR group were informed that another child was alone in an adjoining room and had been warned not to climb up on a chair. The second group was labeled direct responsibility one (DR1). Students in the DR1 group were told the same story as in the IR condition, but was also told that they were left in charge and to take care of anything that happened. The students were given a simple task, and the researcher left the room. The students then heard a loud crash in the adjoining room followed by a minute of sobbing and crying. Students in the third group, direct responsibility two (DR2), had the same instructions as the DR1 group, but the sounds of distress also included calls for help. Ratings from 1 (no help) to 5 (went to the adjoining room) were given to each student by an observer sitting behind a one-way mirror. The ratings are given below. Perform a one-way ANOVA in SPSS with α = .05 and answer the following questions:

PART A: Perform ANOVA analysis using SPSS and present the results in a tabular format (do not copy and paste SPSS’s output).

PART B: Calculate the effect size (w2) and interpret (in words) its meaning.