Math Assignment 3 | Mathematics Homework Help
Question 1 (1 point)
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A research study is investigating the effectiveness of different techniques on teaching writing skills to young children.
Refer to the ANOVA summary table below to identify the confidence coefficient for a hypothesis test conducted at the 95% confidence level.
| Source | SS | df | MS | F |
| Between Treatments | 400.00 | 14 | 28.57 | 7.94 |
| Within Treatments | 90.00 | 25 | 3.6 | |
| Total | 490.00 | 39 |
Use the F-distribution table to find your answer, which should be expressed using two decimal places.
Question 2
A research study is investigating the effectiveness of different techniques on teaching writing skills to young children.
Refer to the ANOVA summary table below to identify the confidence coefficient for a hypothesis test conducted at the 95% confidence level.
| Source | SS | df | MS | F |
| Between Treatments | 400.00 | 25 | 16.00 | 2.16 |
| Within Treatments | 90.00 | 40 | 2.25 | |
| Total | 490.00 | 65 |
Use the F-distribution table to find your answer, which should be expressed using two decimal places.
Question 3 (1 point)
A research study is investigating the effectiveness of different techniques on teaching writing skills to young children.
Refer to the ANOVA summary table below to identify the confidence coefficient for a hypothesis test conducted at the 99% confidence level.
| Source | SS | df | MS | F |
| Between Treatments | 400.00 | 26 | 15.38 | 8.54 |
| Within Treatments | 90.00 | 50 | 1.80 | |
| Total | 490.00 | 76 |
Use the F-distribution table to find your answer, which should be expressed using two decimal places.
Question 4 (1 point)
A research study is investigating the effectiveness of different techniques on teaching writing skills to young children.
Refer to the ANOVA summary table below to identify the confidence coefficient for a hypothesis test conducted at the 95% confidence level.
| Source | SS | df | MS | F |
| Between Treatments | 40.00 | 3 | 13.33 | 6.84 |
| Within Treatments | 80.00 | 41 | 1.95 | |
| Total | 120.00 | 44 |
Use the F-distribution table to find your answer, which should be expressed using two decimal places.
Question 5 (4 points)
A beverage company produces a drink that it wants to ship in 155mL plastic bottles. The machines that dispense the liquid into the bottles on the assembly line must be calibrated so that they do not vary significantly from the 155mL container size, nor from each other. The quality control specialists at the company take a random sample of 3 bottles produced from the four machines used on the assembly line and measure its contents. The results are as follows:
| Machine A | Machine B | Machine C | Machine D |
| 152.3 | 154.5 | 150.5 | 156.6 |
| 151.7 | 155.6 | 151.4 | 155.3 |
| 152.0 | 156.7 | 151.3 | 157.6 |
Calculate the test-statistic (F*) for an ANOVA using this data. Round your answer to 2 decimal
Question 6 (1 point)
A researcher used an analysis of variance (ANOVA) to compare three treatment conditions with separate samples of n = 8 participants in each treatment. The results of the analysis are shown in the following summary table.
| Source | SS | df | MS | F-ratio |
| Between treatments | 4 | |||
| Within treatments | 63 | |||
| Total |
Identify the following missing value from the table: MSB .
Hint: Complete the entire table starting with the df values, then find the value that you have been asked to provide and enter it in the space provided.
Question 7 (1 point)
A researcher used an analysis of variance (ANOVA) to compare three treatment conditions with separate samples of n = 8 participants in each treatment. The results of the analysis are shown in the following summary table.
| Source | SS | df | MS | F-ratio |
| Between treatments | 4 | |||
| Within treatments | 63 | |||
| Total |
Identify the following missing value from the table: SST .
Hint: Complete the entire table starting with the df values, then find the value that you have been asked to provide and enter it in the space provided.
Question 8 (1 point)
A number of new surgery techniques are being tested for their effect on the number of recovery days required by the patient post-operation. A control group is receiving the current treatment, and the other groups are each receiving one of the other new treatment techniques.
The null hypothesis is that all the techniques (the current one and the new ones) are equally as effective (there is no significant difference in the recovery times). The results of the ANOVA used to analyze the data is presented in the table below:
| ANOVA | ||||
| Source of Variation | SS | df | MS | F |
| Between Groups | 15.26 | 3 | 5.09 | 3.70 |
| Within Groups | 21.99 | 16 | 1.37 | |
| Total | 37.25 | 19 |
If a hypothesis test was carried out using α = 0.05, what would be the confidence coefficient? Use two decimal places in your answer.
Question 9 (1 point)
A number of new surgery techniques are being tested for their effect on the number of recovery days required by the patient post-operation. A control group is receiving the current treatment, and the other groups are each receiving one of the other new treatment techniques.
The null hypothesis is that all the techniques (the current one and the new ones) are equally as effective (there is no significant difference in the recovery times). The results of the ANOVA used to analyze the data is presented in the table below:
| ANOVA | ||||
| Source of Variation | SS | df | MS | F |
| Between Groups | 11.00 | 2 | 5.50 | 2.11 |
| Within Groups | 36.53 | 14 | 2.61 | |
| Total | 47.53 | 16 |
If a hypothesis test was carried out using α = 0.01, what would be the confidence coefficient? Use two decimal places in your answer.
Question 10 (1 point)
A number of new surgery techniques are being tested for their effect on the number of recovery days required by the patient post-operation. A control group is receiving the current treatment, and the other groups are each receiving one of the other new treatment techniques.
The null hypothesis is that all the techniques (the current one and the new ones) are equally as effective (there is no significant difference in the recovery times). The results of the ANOVA used to analyze the data is presented in the table below:
| ANOVA | ||||
| Source of Variation | SS | df | MS | F |
| Between Groups | 11.00 | 2 | 5.50 | 2.11 |
| Within Groups | 36.53 | 14 | 2.61 | |
| Total | 47.53 | 16 |
If a hypothesis test was carried out using α = 0.01, what would be the conclusion?
Question 11
A number of new surgery techniques are being tested for their effect on the number of recovery days required by the patient post-operation. A control group is receiving the current treatment, and the other groups are each receiving one of the other new treatment techniques.
The null hypothesis is that all the techniques (the current one and the new ones) are equally as effective (there is no significant difference in the recovery times). The results of the ANOVA used to analyze the data is presented in the table below:
| ANOVA | ||||
| Source of Variation | SS | df | MS | F |
| Between Groups | 15.26 | 3 | 5.09 | 3.70 |
| Within Groups | 21.99 | 16 | 1.37 | |
| Total | 37.25 | 19 |
If a hypothesis test was carried out using α = 0.01, what would be the conclusion?
Question 12 (0.5 points)
A study examined the relationships between income (annual income in $), education (in years), age (in years), and intelligence (IQ) for 40 randomly-selected individuals who work in a particular city.
In studies that examine several variables, the correlations between all possible variable pairings are calculated and presented in correlation matrix.
The correlations between the four variables from this study are presented in the following correlation matrix:
| EDUCATION | AGE | IQ | |
| INCOME | +.62** | +.38* | +.23 |
| EDUCATION | +.06 | +.78** | |
| AGE | -.14 |
n = 40 *p < .01, two tails **p < .05, two tails
Based on the results found in the table, identify the statement that is true.
Question 13 (0.5 points)
A study examined the relationships between income (annual income in $), education (in years), age (in years), and intelligence (IQ) for 40 randomly-selected individuals who work in a particular city.
In studies that examine several variables, the correlations between all possible variable pairings are calculated and presented in correlation matrix.
The correlations between the four variables from this study are presented in the following correlation matrix:
| EDUCATION | AGE | IQ | |
| INCOME | +.62** | +.38* | +.23 |
| EDUCATION | +.06 | +.78** | |
| AGE | -.14 |
n = 40 *p < .01, two tails **p < .05, two tails
Based on the results found in the table, identify the statement that is false.
Question 14 (0.5 points)
A study examined the relationships between income (annual income in $), education (in years), age (in years), and intelligence (IQ) for 40 randomly-selected individuals who work in a particular city.
In studies that examine several variables, the correlations between all possible variable pairings are calculated and presented in correlation matrix.
The correlations between the four variables from this study are presented in the following correlation matrix:
| EDUCATION | AGE | IQ | |
| INCOME | +.62** | +.38* | +.23 |
| EDUCATION | +.06 | +.78** | |
| AGE | -.14 |
n = 40 *p < .01, two tails **p < .05, two tails
Based on the results found in the table, identify the statement that is true.
Question 15 (0.5 points)
A study examined the relationships between income (annual income in $), education (in years), age (in years), and intelligence (IQ) for 40 randomly-selected individuals who work in a particular city.
In studies that examine several variables, the correlations between all possible variable pairings are calculated and presented in correlation matrix.
The correlations between the four variables from this study are presented in the following correlation matrix:
| EDUCATION | AGE | IQ | |
| INCOME | +.62** | +.38* | +.23 |
| EDUCATION | +.06 | +.78** | |
| AGE | -.14 |
n = 40 *p < .01, two tails **p < .05, two tails
Based on the results found in the table, identify the statement that is false.
Question 16 (3 points)
A professor at McGill claims that they can predict the performance of their students on the final exam using their results on the first quiz. They claim that the grades on the two assessments form a strong positive relationship. To test this theory, you randomly select 5 students from the class at the end of the term and examine their performance on the first quiz and on the final exam. The results are as follows:
| Student | Quiz 1 (x) | Final Exam (y) |
| 1 | 6.4 | 88 |
| 2 | 5.3 | 52 |
| 3 | 7.3 | 74 |
| 4 | 9.7 | 98 |
| 5 | 4.0 | 60 |
Calculate the correlation coefficient (r). Round your answer to three decimals.
Question 17 (2 points)
Convinced that a strong positive relationship exists between the performance of a student on their first quiz and on their final exam, the professor scours through several years of class data and randomly samples the performances of 100 students. Here is what they found using that data:
| n | Mean | StDev | |
| Final Exam Scores | 100 | 79.9 | 6.0 |
| Quiz 1 Scores | 100 | 6.8 | 1.1 |
| r = 0.781 |
Use this data to create the linear equation of regression for the line of best fit and predict the final exam score of a student who scored 3.3 on Quiz 1. Round your answer to one decimal.
Hint: Use Quiz 1 as your independent variable (x) and Final Exam as your predicted variable (y)
Question 18 (4 points)
In a continued quest to prove their point, the professor randomly selects 20 students from their most recent version of the course. Use this data to conduct a complete hypothesis test to prove that there is a positive correlation between a student’s Quiz 1 score and their Final Exam score.
Conduct this test using a significance level (α) of 0.05 and mention the coefficient of determination (r2) in your conclusion.
Hint: Recall the four steps of a complete hypothesis test: State the hypothesis, set the criteria for a decision, compute statistics, and make a decision!
| n | Mean | StDev | |
| Quiz 1 Scores | 20 | 6.6 | 2.6 |
| Final Exam Score | 20 | 79.3 | 3.4 |
| r = 0.456 |
Interpretation of an Article
Questions 19-25 will be based on a research study.
In this section, you will be asked to read a brief research article and interpret its results.
Read the short article, Spacing Effects in Real-world Classroom Vocabulary Learning (by Hailey Sobel, Nicholas Cepeda, and Irina Kapler), paying special attention to the Method and Results and Discussion sections, then answer the following question.
What was the final sample size for this study?
Question 20 (0.5 points)
Read the short article, Spacing Effects in Real-world Classroom Vocabulary Learning (by Hailey Sobel, Nicholas Cepeda, and Irina Kapler), paying special attention to the Method and Results and Discussion sections, then answer the following question.
What was the mean score for the students in the spaced condition?
Question 21 (0.5 points)
Read the short article, Spacing Effects in Real-world Classroom Vocabulary Learning (by Hailey Sobel, Nicholas Cepeda, and Irina Kapler), paying special attention to the Method and Results and Discussion sections, then answer the following question.
What was the standard error for the mean for the students in the massed condition?
Question 22 (0.5 points)
Read the short article, Spacing Effects in Real-world Classroom Vocabulary Learning (by Hailey Sobel, Nicholas Cepeda, and Irina Kapler), paying special attention to the Method and Results and Discussion sections, then answer the following question.
When the researchers compared the conditions, what was the value of the test-statistic that was calculated?
Question 23 (0.5 points)
Read the short article, Spacing Effects in Real-world Classroom Vocabulary Learning (by Hailey Sobel, Nicholas Cepeda, and Irina Kapler), paying special attention to the Method and Results and Discussion sections, then answer the following question.
What was the p-value? Make sure that you include all the decimal points!
Question 24 (0.5 points)
Read the short article, Spacing Effects in Real-world Classroom Vocabulary Learning (by Hailey Sobel, Nicholas Cepeda, and Irina Kapler), paying special attention to the Method and Results and Discussion sections, then answer the following question.
What was the effect size (d)? Make sure you include all the decimal points!
Question 25 (2 points)
Considering the answers you have provided about the research article, provide a brief (1-2 sentences) conclusion to this study on behalf of the researchers.
