The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from
Soil water content from field I: x1; n1 = 72
Soil water content from field II: x2; n2 = 80
(a) Use a calculator with mean and standard deviation keys to verify that 1 11.42, s1 2.08, 2 10.65, and s2 3.03.
(b) Let Î¼1 be the population mean for x1 and let Î¼2 be the population mean for x2. Find a 95% confidence interval for Î¼1 - Î¼2.
(c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? All negative? of different signs? At the 95% level of confidence, is the population mean soil water content of the first field higher than that of the second field?
(d) Which distribution (standard normal or Students t) did you use? Why? Do you need information about the soil water content distributions?
(e) Use Î± = 0.01 to test the claim that the population mean soil water content of the first field is higher than that of the second.
For each hypothesis test, please provide the following information:
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level Î±?
(v) Interpret your conclusion in the context of the application.
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