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Statistics Help

**Question: **2) The producers of a new toothpaste claim that it prevents more cavities that 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 checkup is 1.73 (σ = 1.12).

a. Is this a one- or two-tailed test?

This is a one tailed test.

b. What are H0 and Ha for this study?

H0: There is no difference between new and other toothpastes in the mean number of cavities of the general population: 1¼ = 1.73

Ha : New toothpaste reduces cavities compared to other brands I¼ < 1.73

c. Compare Zobt

d. What is Zcv?

e. Should H0 be rejected? What should the researcher conclude?

f. Determine the 95% confidence interval for the population mean, based on the sample mean.

4) Henry performed 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 Type I or Type II error in this situation?

6) a researcher hypothesizes 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. Μ = 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, 61, 60, 59.

a. Is this a one- or two-tailed test?

b. What are H0 and Ha for this study?

c. Compare tobt

d. What is tcv?

e. Should H0 be rejected? What should the researcher conclude?

f. Determine the 95% confidence interval for the population mean, based on the sample mean.

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 a random sample of 120 individuals who live in California and finds that the number who exercises regularly is 31 out of 120.

a) What is X2obt?

b) What is the df for this test?

c) What is X2cv?

d) What conclusion should be drawn from these results?

2) A student is interested in whether students who study with music playing devote as much attention to their studies as do students who study under quiet conditions (he believes that studying under quiet conditions leads to better attention). He randomly participates to either the music or non-music condition and has them read and study the same passage of information for the same amount of time. Subjects are given the same 10-item test on the material. Their scores appear next. Scores on the test represent interval-ratio data and are normally distributed.

Music No Music

7 7

6 8

5 7

6 7

8 9

8 8

a) What statistical test should be used to analyze these data?

b) What are H0 and Ha for this study?

c) Conduct the appropriate analysis.

d) Should H0 be rejected? What should the researcher conclude?

e) If significant, compute and interpret the effect size.

f) If significant draw a graph representing the data.

g) Determine the 95% confidence interval.

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-ration 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

a) What statistical test should be used to analyze these data?

b) What are H0 and Ha for this study?

c) Conduct the appropriate analysis.

d) Should H0 be rejected? What should the researcher conclude?

e) If significant, compute and interpret the effect size.

f) If significant draw a graph representing the data.

g) Determine the 95% confidence interval.

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 green or red sauce condition. Participants indicate the tastiness of the sauce on a 10-point scale. Tastiness scores tend to be skewed. The scores follow:

RED SAUCE GREEN SAUCE

7 4

5 5

9 6

10 8

6 7

7 6

8 9

a) What statistical test should be used to analyze these data?

b) Identify H0 and Ha for this study

c) Conduct the appropriate analysis

d) Should H0 be rejected? What should the researcher conclude?

8) You notice in your introductory psychology class that more 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. Data follow:

Men Women

Front of the room 15 27

Back of the room 32 19

a) What is X2obt?

b) What is the df for this test?

c) What is X2cv?

d) What conclusion should be drawn from these results?

Edit

**Answer: **c. Zobt = (1.73 - 1.5)/(1.12/sqrt(60)) = 1.5906 Edit

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