Part II (30 marks) Solve the following problem using software R: A pH level of the soil between 5.3 and 6.5 is optimal for strawberries. To measure the pH level, a field is divided into two lots. In each lot, we randomly select 20 samples of soil and measure their pHi levels. The data are given in pH.txt, which can be downloaded from Blackboard Learn. A and 6.5 is optimal for strawberries. To measure the pH level, QQ-plot of the data is given on the next page. (a) Based on the QQ-plot, do you think the soil pH levels in the two lots are normally distributed? Do you think the two populations have equal variances? Explain. (b) Let X1, X2 denote the soil pH level in lots 1 and 2 respectively. Suppose you want to test whether the mean pH level in lot 1 is different from the mean pH level in lot 2. State the null and alternative hypotheses using both mathematical and descriptive languages. (c) State the potential Type I and Type II errors for testing (b). (d) Wh ich test statistic should you use for (b)? Give the mathematical expression of the test statistic. What is the sampling distribution for this test statistic? Is the sampling distribution an approximation or an exact one? (e) Carry out the hypothesis test in (b) using R. State your conclusion at significance level hesis test in (b) using R. State your conclusion at significance level = 0.05. Re-state your conclusion at significance level a 0.005.
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