Question

The recommended adequate intake (RAI) of calcium for adults is 1000 mg. per day. To investigate the calcium intake of people living below the poverty level, a researcher obtained a random sample of 18 adults below the poverty level and found a mean daily calcium intake of 947.4 mg.

Required:
a. Determine the margin of error
b. Find 95% confidence interval fo rthe population mean
c. Interpret the confidence inteval. ( explain what it tells us about the estimated mean daily camlium intake for the population).

Answer 1

93.50

(853.90 ; 1040.90)

Explanation:

Mean, xbar = 947.4 mg

Sample size, n = 18

σ = 188

Margin of Error :

Tcritical * σ/√n

TCritical at 95% , df = n - 1 = 17 = 2.11

Margin of Error = 2.11 * 188/√18 = 93.50

The 95%, confidence interval :

Xbar ±Margin of error

Lower boundary = Xbar - margin of error

Lower boundary = 947.4 - 93.50 = 853.90

Upper boundary = Xbar + margin of error

Lower boundary = 947.4 + 93.50 = 1040.90

(853.90 ; 1040.90)