Calcium is essential to tree growth because it promotes the formation of wood an

Question

Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 1990, the concentration of calcium in precipitation in a certain area was 0.12 milligrams per liter (mg/L). A random sample of 10 precipitation dates in 2007 results in the following data table. Complete parts (a) through (c) below. (a) State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990. H_0: 0.12 mg/L H_1: 0.12 mg/L (b) Construct a 95% confidence interval about the sample mean concentration of calcium precipitation. (Use ascending order. Round to four decimal places as needed.) (c) Does the sample evidence suggest that calcium concentrations have changed since 1990? A. Yes, because the confidence interval does not contain 0.12 mg/L B. No, because the confidence interval contains 0.12 mg/L C. Yes, because the confidence interval contains 0.12 mg/L. D. No, because the confidence interval does not contain 0.12 mg/L.

Explanation / Answer

Solution:-

(a) Hypothesis

H0 : = 0.12 mg/L
H1 : 0.12 mg/L

(b) Formula to calculate 95% confidence interval

Here, in the question standard deviation is not given, I am assuming it to be 0.1, if it is different kindly plug in the calculations below, where you see 0.1.

M = 0.12
t = 1.96 (using t-value table for 95% CI)
sM = (0.12/10) = 0.03

= M ± Z(sM)
= 0.12 ± 1.96*0.03
= 0.12 ± 0.062

95% CI [0.058, 0.182]

(c) Yes, because the confidence interval contains 0.12 mg/L.

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