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Jackson even-numbered Chapter exercises (pp. 220-221; 273-275) PAGE 220-221 2a. The producers of a new toothpaste claim that it prevents more cavities than other brands of

  1. Jackson even-numbered Chapter exercises (pp. 220-221; 273-275)

PAGE 220-221
2a. The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people used the new toothpaste for 6-months. The mean number of cavities at their next checkup is 1.5. In the general population, the mean number of cavities at a 6-month check-up is 1.73 (0=1.12)

  1. Is this a one or two-tailed test?
  2. What are the H0 and Ha for this study?
  3. Compute Zobt-
  4. What is Zev?

4a. Henry preformed a two-tailed test for an experiment in which N-24. He could not find his table of t critical values, but he remembered the tcv at df=13. He decided to compare his tobtwith this tcv. Is he more likely to make a Type I or a Type II error in this situation?
6a. A researcher hypothesis that individuals who listen to classical music will score differently from the general population on a test of spatial ability. On a standardized test of spatial ability, u=58. A random sample of 14 individuals who listen to classical music is given the same test. Their scores on the test are 52,59,63,65,58,55,62,63,53,59,57,61,60,59.

  1. Is this a one or two-tailed test?
  2. What are the Ho and Ha for this study?
  3. Compute t-obt-
  4. What is tcv?
  5. Should Ho be rejected? What should the researcher conclude?
  6. Determine the 95% confidence interval for the population mean, based on the sample mean.

8a. A researcher believes that the percentage of people who exercise in California is greater than the national exercise rate. The national rate is 20%. The researcher gathers random sample of the 20 individuals who live in California and finds that the number who exercise regularly is 31 out of 120.

  1. What is the obt?
  2. What is the df for this test?
  3. What is the cv?
  4. What conclusion should be drawn from these results?

PAGE 274-275

  1. The researcher in exercise 2 decides to conduct the same study using a within-participants design to control for differences in cognitive ability. He selects a random sample of subjects and has them study different material of equal difficulty in both the music and no music conditions. The study is completely counterbalanced to control for order effects. The data appear next. As before, they are measured on an interval-ratio scale and are normally distributed; he believes that studying under quiet conditions will lead to better performance.

MUSIC             NO MUSIC
7                       7
6                       8
5                       7
6                       7
8                     9
8                       8

  1. What statistical test should be used to analyze these data?
  2. Identify Ho and Ha for this study.
  3. Conduct the appropriate analysis.
  4. Should Ho be rejected? What should the researcher conclude?
  5. If significant, compute and interpret the effect size.
  6. If significant, draw a graph representing the data.
  7. Determine 95% confidence interval.
  8. Researchers at a food company are interested in how a new spaghetti sauce made from green tomatoes (and green in color) will compare to their traditional red spaghetti sauce. They are worried that the green color will adversely affect the tastiness scores. They randomly assign subjects to either the green or the red sauce condition. Participants indicate the tastiness of the sauce on a 10-point scale. Tastiness scores tend to be skewed. The scores are as follows.

Red Sauce   Green Sauce
7                     4
6                              5
9                              6
10                            8
6                              7
7                              6
8                              9
 

  1. What statistical test should be used to analyze these data?
  2. Identify Ho and Ha for this study.
  3. Conduct the appropriate analysis.
  4. Should Ho be rejected? What should the researcher conclude?

 

  1. You notice in your introductory psychology class that women tend to sit up front, and more men sit in the back. To determine whether this difference is significant, you collect data on the seating preferences for the students in your class. The data follow.

 
                                     Men           Women
Front of the Room         15                                      27
Back of the Room         32                                       19
 

  1. What is the obt?
  2. What is the dffor this test?
  3. What is the cv?
  4. What conclusion should be drawn from these results?
  5. What are degrees of freedom? How are the calculated?
  6. What do inferential statistics allow you to infer?
  7. What is the General Linear Model (GLM)? Why does it matter?
  8. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?
  9. Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?
  10. Part II introduces you to a debate in the field of education between those who support Null Hypothesis Significance Testing (NHST) and those who argue that NHST is poorly suited to most of the questions educators are interested in. Jackson (2012) and Trochim and Donnelly (2006) pretty much follow this model. Northcentral follows it. But, as the authors of the readings for Part II argue, using statistical analyses based on this model may yield very misleading results. You may or may not propose a study that uses alternative models of data analysis and presentation of findings (e.g., confidence intervals and effect sizes) or supplements NHST with another model. In any case, by learning about alternatives to NHST, you will better understand it and the culture of the field of education.

 

  1. What are degrees of freedom? How are they calculated?
  2. What do inferential statistics allow you to infer?
  3. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?
  4. Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?
  5. What does p = .05 mean? What are some misconceptions about the meaning of p =.05? Why are they wrong? Should all research adhere to the p = .05 standard for significance? Why or why not?
  6. Compare and contrast the concepts of effect size and statistical significance.
  7. What is the difference between a statistically significant result and a clinically or “real world” significant result? Give examples of both.
  8. What is NHST? Describe the assumptions of the model.
  9. Describe and explain two alternatives to NHST. What do their proponents consider to be their advantages?
  10. Which type of analysis would best answer the research question for your stated topic of interest? Justify your answer.
  11. Question 2a
    The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste.  A random sample of 60 people used the new toothpaste for 6-months.  The mean number of cavities at their next checkup is 1.5.  In the general population, the mean number of cavities at a 6-month check-up is 1.73)

    • Is this a one or two-tailed test?
    • What are the H0 and Ha for this study?
    • Compute Zobt-
    • What is Zcv?
    • Question 4Henry preformed a two-tailed test for an experiment in which N=24.  He could not find his table of t critical values, but he remembered the tcv at df=13. He decided to compare his tobt with this tcv.  Is he more likely to make a Type I or a Type II error in this situation?
    • Question 6
      A researcher hypothesis that individuals who listen to classical music will score differently from the general population on a test of spatial ability.  On a standardized test of spatial ability, u=58.  A random sample of 14 individuals who listen to classical music is given the same test.  Their scores on the test are 52,59,63,65,58,55,62,63,53,59,57,61,60,59.

      • Is this a one or two-tailed test?
      • What are the Ho and Ha for this study?
      • Compute t-obt-
      • What is tcv?
      • Should Ho be rejected? What should the researcher conclude?
      • Determine the 95% confidence interval for the population mean, based on the sample mean.
    • Question 8
      A researcher believes that the percentage of people who exercise in California is greater than the national exercise rate.  The national rate is 20%. The researcher gathers random sample of the 120 individuals who live in California and finds that the number who exercise regularly is 31 out of 120.

      • What is the obt?
      • What is the df for this test?
      • What is the cv?
      • What conclusion should be drawn from these results?
    • Question 4
      The researcher in exercise 2 decides to conduct the same study using a within-participants design to control for differences in cognitive ability.  He selects a random sample of subjects and has them study different material of equal difficulty in both the music and no music conditions.  The study is completely counterbalanced to control for order effects.  The data appear next.  As before, they are measured on an interval-ratio scale and are normally distributed; he believes that studying under quiet conditions will lead to better performance.

      • What statistical test should be used to analyze these data?
      • Identify Ho and Ha for this study.
      • Conduct the appropriate analysis.
      • Should Ho be rejected? What should the researcher conclude?
      • If significant, compute and interpret the effect size.
      • If significant, draw a graph representing the data.
      • Determine 95% confidence interval.
    • Question 6
      Researchers at a food company are interested in how a new spaghetti sauce made from green tomatoes (and green in color) will compare to their traditional red spaghetti sauce.  They are worried that the green color will adversely affect the tastiness scores.  They randomly assign subjects to either the green or the red sauce condition.  Participants indicate the tastiness of the sauce on a 10-point scale.  Tastiness scores tend to be skewed.  The scores are as follows.

      • What statistical test should be used to analyze these data?
      • Identify Ho and Ha for this study.
      • Conduct the appropriate analysis.
      • Should Ho be rejected? What should the researcher conclude?
    • Question 8 
      You notice in your introductory psychology class that women tend to sit up front, and more men sit in the back.  To determine whether this difference is significant, you collect data on the seating preferences for the students in your class.  The data follow.
                                           Men           Women
      Front of the Room         15                  27
      Back of the Room          32                  19

      • What is the obt?
      • What is the df for this test?
      • What is the cv?
      • What conclusion should be drawn from these results?
    • Question 2
      What are degrees of freedom? How are the calculated?
    • Question 3 
      What do inferential statistics allow you to infer?
    • Question 4 
      What is the General Linear Model (GLM)? Why does it matter?
    • Question 5
      Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?
    • Question 6 
      Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?
    • Part II Assignment
      What does p = .05 mean?  What are some misconceptions about the meaning of p =.05?  Why are they wrong?  Should all research adhere to the p = .05 standard for significance?  Why or why not?
    • What is the difference between a statistically significant result and a clinically or “real world” significant result?  Give examples of both.
    • What is NHST?  Describe the assumptions of the model.
    • Describe and explain two alternatives to NHST. What do their proponents consider to be their advantages?
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