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21 . In a sample of 25 cases, two variables have a correlation of 0.45. Do a
t -test to see if this result is significant at the
α = 0.05 level. Use the formula:
$t=\frac{r\sqrt{n-2}}{\sqrt{1-{r}^{2}}}$
Use the following information to answer the next two exercises. A study relating the grams of potassium (
Y ) to the grams of fiber (
X ) per serving in enriched flour products (bread, rolls, etc.) produced the equation:
$\widehat{y}=25+16x$
22 . For a product with five grams of fiber per serving, what are the expected grams of potassium per serving?
23 . Comparing two products, one with three grams of fiber per serving and one with six grams of fiber per serving, what is the expected difference in grams of potassium per serving?
24 . In the context of regression analysis, what is the definition of an outlier, and what is a rule of thumb to evaluate if a given value in a data set is an outlier?
25 . In the context of regression analysis, what is the definition of an influential point, and how does an influential point differ from an outlier?
26 . The least squares regression line for a data set is $\widehat{y}=5+0.3x$ and the standard deviation of the residuals is 0.4. Does a case with the values x = 2, y = 6.2 qualify as an outlier?
27 . The least squares regression line for a data set is $\widehat{y}=2.3-0.1x$ and the standard deviation of the residuals is 0.13. Does a case with the values x = 4.1, y = 2.34 qualify as an outlier?
28 . What are the five basic assumptions to be met if you want to do a one-way ANOVA?
29 . You are conducting a one-way ANOVA comparing the effectiveness of four drugs in lowering blood pressure in hypertensive patients. What are the null and alternative hypotheses for this study?
30 . What is the primary difference between the independent samples t -test and one-way ANOVA?
31 . You are comparing the results of three methods of teaching geometry to high school students. The final exam scores
X
_{1} ,
X
_{2} ,
X
_{3} , for the samples taught by the different methods have the following distributions:
X
_{1} ~
N (85, 3.6)
X
_{1} ~
N (82, 4.8)
X
_{1} ~
N (79, 2.9)
Each sample includes 100 students, and the final exam scores have a range of 0–100. Assuming the samples are independent and randomly selected, have the requirements for conducting a one-way ANOVA been met? Explain why or why not for each assumption.
32 . You conduct a study comparing the effectiveness of four types of fertilizer to increase crop yield on wheat farms. When examining the sample results, you find that two of the samples have an approximately normal distribution, and two have an approximately uniform distribution. Is this a violation of the assumptions for conducting a one-way ANOVA?
Use the following information to answer the next seven exercises. You are conducting a study of three types of feed supplements for cattle to test their effectiveness in producing weight gain among calves whose feed includes one of the supplements. You have four groups of 30 calves (one is a control group receiving the usual feed, but no supplement). You will conduct a one-way ANOVA after one year to see if there are difference in the mean weight for the four groups.
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