Please note that for all problems in this course, the standard cut-off (alpha) for a test of significance will be .05, and you always report the exact power unless SPSS output states p=.000 (you’d report p<.001). Also, remember when hand-calculating, always use TWO decimal places so that deductions in grading won’t be due to rounding differences.

1. What is the dependent variable and its scale of measurement in this scenario? (3 pts)

2. State the independent variable(s) in the scenario and label as either “BS” (between subjcts) or “WS” (within subjects). (2 pts)

3. Paste appropriate SPSS output. (3 pts)

4. Paste appropriate SPSS graph(s), formatted in APA (2 pts). Write an appropriate figure caption using APA format for each figure (begin numbering with 1 – e.g., Figure 1). (2 pts per graph + 2 pts per caption = 8 pts total for this question).

5. Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and a decision about each null hypothesis tested. Include effect sizes, post hoc analyses / interpretations, and refer the reader to Figure(s) created above, when appropriate (4 pts).

6. Identify a potential confounding variable with the study as it was presented (you can use your imagination!). Justify why you think it may be a confound rather than an extraneous variable. (2 pts)

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg).
x 27 42 31 47 23 40 34 52

y 33 21 24 13 29 17 21 14

Complete parts (a) through (e), given Σx = 296, Σy = 172, Σx2 = 11,652, Σy2 = 4042, Σxy = 5917, and r ≈ −0.911. (a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =2 Σy =3 Σx2 =4 Σy2 =5 Σxy =6 r =7

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = ___ y = ___ = y____ + ____x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 = _______ explained _____ % unexplained ______ %

(f) Suppose a car weighs x = 39 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.) ________mpg

Assess this statement using ANOVA: "People with different levels of education exercise for different amounts of time during the week."

Describe which ANOVA test you used and present the main results, including explaining the within and between subjects variation and the F-ratio from the ANOVA table. Discuss whether there is a statistically significant difference between education groups and the amount of exercise.

The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's GPA.

Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:

Type I rooms do not have wireless Internet access and are not available for the Business rental class.

Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 140 rentals in the Super Saver class, 50 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 110 Type I rooms and 110 Type II rooms.

1. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types.

2. How many reservations can be accommodated in each rental class?

You have brown, pink, black, and white socks in a drawer (8 of each color). In each of the following cases, what is the minimum number that you must take out to ensure that:

a) You have a matching pair?

b) You have two of different colors?

c) You have at least 3 brown or 4 pink or 5 black or 7 white socks?

Problem 2

A random sample of 41 business days, from 2016 through 2017, of the closing price of Apple stock is conducted. The sample produces an average closing price of $116.16 with a standard deviation of $10.27.

1. Verify the requirements for the confidence interval.
2. For a 95% confidence interval, find the margin of error for the true average closing price of Apple stock from 2016 through 2017.
3. Interpret a 95% confidence interval for the true average closing price of Apple stock from 2016 through 2017.
4. Respond to the statement that the true average closing price of Apple stock from 2016 through 2017 was less than $125 . Make your response understandable to someone not in the class

The following data represent a sample of the assets (in millions of dollars) of 28 credit unions in a state. Assume that the population in this state is normally distributed with σ=3.5 million dollars. Use Excel to find the 99% confidence interval of the mean assets in millions of dollars. Round your answers to three decimal places and use ascending order.

Assets
12.23
2.89
13.19
73.25
11.59
8.74
7.92
40.22
5.01
2.27
16.56
1.24
9.16
1.91
6.69
3.17
4.78
2.42
1.47
12.77
4.39
2.17
1.42
14.64
1.06
18.13
16.85
21.58

Provide your answer below:        (    ,    )

The following data was collected to explore how the number of square feet in a house, the number of bedrooms, and the age of the house affect the selling price of the house. The dependent variable is the selling price of the house, the first independent variable (x1x1) is the square footage, the second independent variable (x2x2) is the number of bedrooms, and the third independent variable (x3x3) is the age of the house.

Copy Data

Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

If the relationship is statistically significant, indicate the multiple regression equation that best fits the data, rounded to 3 decimal places.

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are not independent. H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are independent.     H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are independent. H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes No    

What sampling distribution will you use?

Student's t chi-square     uniform binomial normal

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100 0.050 < p-value < 0.100     0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent. At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.    

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.368.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.409.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²     H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. The populations follow independent normal distributions. We have random samples from each population.     The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.200 0.100 < p-value < 0.200     0.050 < p-value < 0.100 0.020 < p-value < 0.050 0.002 < p-value < 0.020 p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots. Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.     Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots. Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are different. H₀: The distributions are different.
H₁: The distributions are the same.     H₀: The distributions are the same.
H₁: The distributions are different. H₀: The distributions are the same.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


Are all the expected frequencies greater than 5?

Yes No    

What sampling distribution will you use?

uniform chi-square     binomial normal Student's t

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.100 0.050 < P-value < 0.100     0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population. At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.    

How does gender and occupational prestige affect credibility? Graduate students in a public health program are asked to rate the strength of a paper about the health risks of childhood obesity. In reality, all student raters are given the same paper, but the name and degree associated with the author are changed. The student raters are randomly assigned to one group from the following name ("John Lake", "Joan Lake") and degree (M.D., R.N., Ph.D.) combination. The raters score the paper from 1 to 5 on clarity, strength of argument, and thoroughness. The total scores (the sum of the three scores) are given in the table below. What can be concluded with an α of 0.05?

Compute the corresponding effect size(s) and indicate magnitude(s).
Name: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  

Degree: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  
Interaction: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  

High-profile legal cases have many people reevaluating the jury system. Many believe that juries in criminal trials should be able to convict on less than a unanimous vote. To assess support for this idea, investigators asked each individual in a random sample of Californians whether they favored allowing conviction by a 10–2 verdict in criminal cases not involving the death penalty. A newspaper article reported that 72% supported the 10–2 verdict. Suppose that the sample size for this survey was n = 900.Compute a 99% confidence interval for the proportion of Californians who favor the 10–2 verdict.

Interpret the interval.

We are confident that 99% of the proportion of Californians who favor the 10–2 verdict is within this interval.

We are 99% confident that the proportion of all people who favor the 10–2 verdict is within this interval.    

We are confident that the proportion of all people who favor the 10–2 verdict is within this interval at least 99% of the time.

We are 99% confident that the proportion of Californians who favor the 10–2 verdict is within this interval.