The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste, statistics homework help

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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?


  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?

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Explanation & Answer

Hello again,Attached is the word document containing the complete solution for this assignment. All graphs, charts, formulae, and data are appropriately displayed to answer each question.Thank you again for choosing me! Please let me know if you have any questions.

2a)
1) One-tailed test
2) H0: ΞΌ = 1.73
Ha: ΞΌ < 1.73
βˆ—
3) π‘§π‘œπ‘π‘‘
=

π‘₯Μ… βˆ’πœ‡
𝜎/βˆšπ‘›

=

1.5βˆ’1.73
1.12/√60

= βˆ’1.59

4) zcv = -1.645 for a left-tailed test of a mean with alpha= 0.05
4a) Type II error
6a)
1) Two-tailed test
2) H0: ΞΌ = 58
Ha: ΞΌ β‰  58
3) Tobt = 0.98
4) tcrit = 2.145
5) The decision rule is to reject the null hypothesis is the calculated t-value is > t-crit. In our
case, tobt(0.98) Ξ± = 0.05. Therefore, we do not
reject the null hypothesis. The mean scores for the two groups are different.
5) The effect size is r2, calculated by the following formula:
π‘Ÿ2 =

π‘Ÿ2 =

𝑑2
𝑑 2 +4

where 𝑑 =

2𝑑
βˆšπ‘›βˆ’1

(βˆ’1.68)2
οΏ½...


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