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 0.11 milligrams per liter (mg/L). A random sample of 10 precipitation dates in 2007 results in the following data table.

Data: 0.068 0.084 0.059 0.278 0.117 0.172 0.109 0.218 0.337 0.092

Complete parts (a) through (c) below.

(a) State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990. H0: μ = 0.11 mg/L H1: μ ≠ 0.11 mg/L

(b) Construct a 95% confidence interval about the sample mean concentration of calcium precipitation. The lower bound is______ . The upper bound is______ . (Round to four decimal places as needed.)

(c)

A. No, because the confidence interval contains 0.11 mg/L.

B. No, because the confidence interval does not contain 0.11 mg/L.

C. Yes, because the confidence interval contains 0.11 mg/L.

D. Yes, because the confidence interval does not contain 0.11mg/L.

Answer 1

Solution :

Given that,

0.068, 0.084, 0.059, 0.278 ,0.117, 0.172, 0.109, 0.218, 0.337 ,0.092

n = 10

= = 1.534 / 10 = 0.1534

s² =  (x - )² / n - 1 = 0.0954

Point estimate = sample mean = = 0.1534

sample standard deviation = s = 0.0954

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

(a)

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0.11

H_a :    0.11

(b)

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,9 = 2.262

Margin of error = E = t_/2,df * (s /n)

= 2.262 * (0.0954 / 10)

= 0.0682

The 95% confidence interval estimate of the population mean is,

- E < < + E

0.1534 - 0.0682 < < 0.1534 + 0.0682

0.0852 < < 0.2216

(0.0852 , 0.2216)

Lower bound = 0.0852

Upper bound = 0.2216

(c)

C. Yes, because the confidence interval contains 0.11 mg/L.