Calculus and Above

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1.

Define the term standard deviation. Why is it important to know the standard deviation for a given sample? What do researchers learn about a normal distribution from knowledge of the standard deviation? A sample of n=20 has a mean of M = 40. If the standard deviation is s=5, would a score of X= 55 be considered an extreme value? Why or why not?

Hypothesis testing allows researchers to use sample data, taken from a larger population, to draw inferences (i.e., conclusions) about the population from which the sample came. Hypothesis testing is one of the most commonly used inferential procedures. Define and thoroughly explain the terms null hypothesis and alternative hypothesis. How are they used in hypothesis testing?

Define the term standard error. Why is the standard error important in research using sample distributions? Consider the following scenario: A random sample obtained from a population has a mean of µ=100 and a standard deviation of σ = 20. The error between the sample mean and the population mean for a sample of n = 16 is 5 points and the error between a sample men and population mean for a sample of n = 100 is 2 points. Explain the difference in the standard error for the two samples.

2.

Mary is planning a study to see if learning of 6th graders on a math lesson is affected by background noise level. She wants to use a t-test for independent groups to analyze her results. Help her plan her study. What is her independent variable (IV) here? Describe two conditions she could create for the IV in her study. What is her dependent variable (DV) here? Describe a way to measure the DV so that each participant would have one score at the end. Would this DV measure be on a continuous scale of measurement? Why is this important? Explain and justify.

3.

Consider Mary's experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study? What is the alternative hypothesis for her study? What are the assumptions that must be met about her data before she can correctly use an independent t-test to test the hypotheses? Why? How would she see if her data meet these assumptions? How much room does she have to violate any of these assumptions and still get accurate results from the t-test? Explain and support your answers.

4.

Review the SPSS output file which reports the results of the independent t-test to compare the mean price per 6-pack for regular vs. reduced calorie brands of wheat beer. Answer the following questions based on your observations of the SPSS output file:

Is the F-value for Levene's Test for Equality of Variances significant (that is, is the p < .05)? What is the exact significance level? Note: if the Levene's Test for Equality of Variances is significant, then equal variances cannot be assumed.

Which t-value should you use now that you know whether or not equal variances can be assumed? What is that t-value?

What is the two-tailed significance level for that t-value? State the exact significance value. Report the results of the t-test as follows: t(df value) = ___, and p-value.

Is there a statistically significant difference between the price per 6-pack of regular beers versus reduced calorie beers?

The links to the information for question 4 is below...Thanks

http://www.sendspace.com/file/0zg2l8

http://www.sendspace.com/file/lbro5l

1.

Define the term standard deviation. Why is it important to know the standard deviation for a given sample? What do researchers learn about a normal distribution from knowledge of the standard deviation? A sample of n=20 has a mean of M = 40. If the standard deviation is s=5, would a score of X= 55 be considered an extreme value? Why or why not?

Hypothesis testing allows researchers to use sample data, taken from a larger population, to draw inferences (i.e., conclusions) about the population from which the sample came. Hypothesis testing is one of the most commonly used inferential procedures. Define and thoroughly explain the terms null hypothesis and alternative hypothesis. How are they used in hypothesis testing?

Define the term standard error. Why is the standard error important in research using sample distributions? Consider the following scenario: A random sample obtained from a population has a mean of µ=100 and a standard deviation of σ = 20. The error between the sample mean and the population mean for a sample of n = 16 is 5 points and the error between a sample men and population mean for a sample of n = 100 is 2 points. Explain the difference in the standard error for the two samples.

2.

Mary is planning a study to see if learning of 6th graders on a math lesson is affected by background noise level. She wants to use a t-test for independent groups to analyze her results. Help her plan her study. What is her independent variable (IV) here? Describe two conditions she could create for the IV in her study. What is her dependent variable (DV) here? Describe a way to measure the DV so that each participant would have one score at the end. Would this DV measure be on a continuous scale of measurement? Why is this important? Explain and justify.

3.

Consider Mary's experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study? What is the alternative hypothesis for her study? What are the assumptions that must be met about her data before she can correctly use an independent t-test to test the hypotheses? Why? How would she see if her data meet these assumptions? How much room does she have to violate any of these assumptions and still get accurate results from the t-test? Explain and support your answers.

4.

Review the SPSS output file which reports the results of the independent t-test to compare the mean price per 6-pack for regular vs. reduced calorie brands of wheat beer. Answer the following questions based on your observations of the SPSS output file:

Is the F-value for Levene's Test for Equality of Variances significant (that is, is the p < .05)? What is the exact significance level? Note: if the Levene's Test for Equality of Variances is significant, then equal variances cannot be assumed.

Which t-value should you use now that you know whether or not equal variances can be assumed? What is that t-value?

What is the two-tailed significance level for that t-value? State the exact significance value. Report the results of the t-test as follows: t(df value) = ___, and p-value.

Is there a statistically significant difference between the price per 6-pack of regular beers versus reduced calorie beers?

The links to the information for question 4 is below...Thanks

http://www.sendspace.com/file/0zg2l8

http://www.sendspace.com/file/lbro5l

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