A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of α = 0.05 is chosen.
-
- (a) State hypotheses appropriate to the research question.
- (b) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
- (c) Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
- (d) Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
- (e) Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of α = 0.05 is chosen.
-
- (a) State hypotheses appropriate to the research question.
- (b) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
- (c) Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
- (d) Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
- (e) Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?
Related textbook solutions
Related questions
Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.
The students receive the following arithmetic test scores:
| Cola | Black Tea | Coffee | ||
| Caffeine Content (mg/oz) | 2.9 | 5.9 | 13.4 | |
| 85 | 85 | 92 | ∑X2 = 147,641 | |
| 86 | 89 | 87 | G = 1,755 | |
| 82 | 82 | 80 | N = 21 | |
| 75 | 75 | 89 | k = 3 | |
| 66 | 88 | 96 | ||
| 78 | 76 | 83 | ||
| 87 | 82 | 92 | ||
| T1 = 559 | T2 = 559 | T3 = 559 | ||
| SS1 = 338.86 | SS2 = 338.86 | SS3 = 338.86 | ||
| n1 = 7 | n2 = 7 | n3 = 7 | ||
| M1 = 79.8571 | M2 = 79.8571 | M3 = 79.8571 |
1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?
(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.
(b) The population mean test scores for all three treatments are equal.
(c) The population mean test scores for all three treatments are different.
(d) The population mean test scores for all three treatments are not all equal.
2.) Calculate the degrees of freedom and the variances for the following ANOVA table:
| Source | SS | df | MS |
| Between | - | - | - |
| Within | 702.28 | - | - |
| Total | 973.14 | - |
The formula for the F-ratio is:
3.) Using words, the formula of the F-ratio can be written as:
4.) Using the data from the ANOVA table given, the F-ratio can be written as:
5.) Calculate for F-ratio:
6.) At the 
(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.
(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
(d)You can reject the null hypothesis; caffeine does appear to affect test performance.
