Question

Use the following information to answer the next three questions. Civil engineers collected data from one area of Calgary on the amount of salt (in tons) used to keep highways drivable during a snowstorm. The amount of salt for n=10 snowstorms were as follows: 1111, 2215, 1573, 2813, 2815, 2126, 854, 3965, 1819, 776. Find a 95% confidence interval for the true population mean amount of salt required in a snowstorm.

1) What is the margin of error for this CI?

2) Lower bound ?

3) Upper bound?

Answer 1

For finding confidence interval first we need to find mean and standard deviation:

Mean Calculation

Mean = Sum of all terms/No. of Terms

Sum of all terms = 1111 + 2215 + 1573 + 2813 + 2815 + 2126 + 854 + 3965 + 1819 + 776

Sum of all terms = 20067

No. of temrs = 10

Mean = 20067/10 = 2006.7

Standard Deviation Calculation

We can compute standard deviation in 4 steps:

Step 1: Find the mean.

In this case Mean =2006.7

Step 2: Create the following table.

Step 3: Find the sum of numbers in the last column to get.

∑(Data−Mean)² = 9064974.1

Step 4: Calculate standard deviation using the above formula.

SD = SQRT(9064974.1/(10-1))

SD = 1003.6032

Confidence Interval Calculation

Confidence Interval Formula:

Step 1: Find α/2
Level of Confidence = 95%
α = 100% - (Level of Confidence) = 5%
α/2 = 2.5% = 0.025

Step 2: Find t_α/2
Calculate t_α/2 by using t-distribution with degrees of freedom (DF) as n - 1 = 10 - 1 = 9 and α/2 = 0.025 as right-tailed area and left-tailed area.

t_α/2 = 2.262157 (Obtained using online t value calcualtor for df = 9 and α/2 = 0.025 )

Step 3: Calculate Confidence Interval

Margin of Error = t_α/2•(s/√n) = (2.262157)(1003.6032/√10) = 717.934

Lower Bound = x̄ - t_α/2•(s/√n) = 2006.7 - 717.934 = 1288.766

Upper Bound = x̄ + t_α/2•(s/√n) = 2006.7 + 717.934 = 2724.634