ETR 521 Lab 2 (30 points)

Please turn in this graded lab before the beginning of class on November 7th . You can work by yourself or in groups of 2, 3, or 4 students. If you work with other students, all of you will receive the same score. Please type up this lab and attach the print outs of your work (e.g., results, graphs, etc.).

Part I: A random sample of 10 students in a 4th grade reading class was tested to determine reading speed and reading comprehension. Based on a fixed-length standardized test reading passage, the following speeds (in minutes) and comprehension scores (based on a 100-point scale) were obtained ( 7 points ).

Reading

Speed 5 7 15 12 8 7 10 11 13 9

Reading 60 76 96 100 81 75 85 88 98 83

Comprehension

Using SPSS, answer the following questions. Include your output .

1. Conduct a hypothesis test to determine if these students’ reading speeds differ from a speed of 6 and obtain a 95% confidence interval. State the null and alternative hypotheses, list the tabled critical value of the t at the .05 alpha level, the value of the observed sample test statistic, the sample p-value, and state your conclusions/answer in the context of the original problem being examined (2).
2. List and give an interpretation of the 95% confidence interval in part a (1).
3. Conduct a hypothesis test to determine if reading comprehension for these students, which is known in the population to be < 77, is > 77 and obtain a 95% confidence interval. State the null and alternative hypotheses, list the tabled critical value of the t at the .05 alpha level, the value of the observed sample test statistic, the sample p-value, and state your conclusions (2).
4. For both of these tests , list your assumptions for running them, print out a histogram with a normal curve for each, list the skewness and kurtosis values for both, and discuss whether the assumptions are fine for these data according to what the graphs and skewness and kurtosis values depict (2).

Part II:

1. It has been estimated that lead poisoning resulting from an unnatural craving for substances, such as paint, may affect as many as a quarter of a million children each year causing them to suffer from severe, irreversible brain-related harm and damage. Explanations for why children consume lead can range from improper parental supervision to a child’s need to "mouth" objects. Some researchers, however, have been investigating whether the habits of eating such substances had a nutritional explanation. One study looked at the difference between a regular diet and a calcium-deficient diet on the

ingestion of a lead-acetate solution in rats. Each rat in a group of 20 rats was assigned randomly to either an experimental or control group. Those in the control group received a normal diet, while the experimental group received a calcium-deficient diet. Each of the rats occupied a separate cage and was monitored to observe the quantity of a . 15% lead-acetate solution consumed during the study period ( 7 points ). The results were:

1. First, list your assumptions for this test, print out the graphs, the skewness and kurtosis values for both, and discuss whether the assumptions are fine for these data according to: 1). what the graphs and skewness and kurtosis values depict and 2). what was found in the Levene’s test data (2).
2. Conduct the test. State the null and alternative hypotheses, list the tabled critical value of the t at the .05alpha level, the value of the sample test statistic, the sample p-value, and what conclusions can be reached (2).
3. What does the confidence interval from the output indicate about the difference in the means (1)?
4. List the standard error of the difference (SED). Explain what the SED value means (1)?
5. Using the Effect Size Calculator on our course website, or if you prefer to hand calculate, determine the effect size for this problem and explain what the result means (1).

Part III : Insurance adjusters are concerned about the estimates they are receiving from Garage I for auto repairs compared to Garage II. It was thought by the industry that the two estimates were equal, but that may not be the case. To verify their suspicions, each of 15 cars involved recently in an accident was taken to both garages for separate estimates to determine if the garages differed based on their repair costs ( 6 points ).

Note: These estimates are in hundreds of dollars. Enter these data into SPSS.

1. State the null and alternative hypotheses, list the tabled critical value of the t at the .01 alpha level, the value of the sample test statistic, the sample p-value, and what conclusions can be reached (2).
2. Looking at the Paired Samples Correlations data, should these data be paired and explain what the information in the Correlation box and the Significance box indicate (1).
3. Change the confidence interval to 99%, list and interpret this interval (1).
4. Using the Effect Size Calculator on our course website, or if you prefer to hand calculate, determine the effect size for this problem and explain what the result means (1).
5. For this test, the assumption that must be met is that the differences must not be too skewed. To look at the differences, go to Transform – Compute, type in a name such as difference in the Target Variable box. In the Expression box, move over the variable for Garage I, a minus sign, and then move over the variable for Garage II. Choose OK – you have now created a new variable of the differences. Print out a simple boxplot of the summary of a separate variable, the skewness and kurtosis values for this measure, and discuss whether the assumption is met, or not, based on these data (1).

Part IV: The yields, in pounds, of five different varieties (i.e., 1, 2, 3, 4, 5) of four-year old orange trees in one orchard are to be compared. A random sample of seven trees of each variety was obtained from the orchard. The yields for these trees are presented here ( 10 points ):

1. Go into Explore and put in the DV (i.e., Dependent) by the IV (i.e., Factor) and click on Statistics and Plots (you can undo the Stem and Leaf default to cut down on paper usage). You should produce skew and kurtosis data, along with a single boxplot showing Yields by Tree type. Looking at these numerical and pictorial data, explain what you see in terms of distribution of the data and if we have covered initially some our assumptions to run an ANOVA (2).
2. State the null and alternative hypotheses for the Test of Homogeneity of Variance, after running an ANOVA for these data, list the results for this test, and what do the results mean in terms of our major assumption for this test (2)?
3. State the null and alternative hypotheses for the ANOVA, list the tabled F critical value at the .05 alpha level, the value of the sample F statistic, the value of the p-value affiliated with the sample F statistic, and what conclusion can be reached about the test conducted (2).
4. Square root the Mean Square Within Groups value. What does this value mean for the overall model (1)?
5. If the sample F statistic was statistically significant, what post-hoc tests did you run and list the pair(s) of mean(s) that were statistically significant (1).
6. List the effect size and explain what it means for the overall model (1).
7. List the power value and explain what it means for the overall model (1).

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Solution: The downloadable solution consists of 29 pages, 2347 words and 29 charts.
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