Question

Provide an original example using the one-mean t-interval procedure (population standard deviation unknown). For this example, provide the following items:

• Describe the assumptions that must be met before using this procedure.
• Compute the confidence interval for a 95% confidence level. Show all work.

Answer 1

Example with a solution:

Let a researcher wants to estimate the TDS level of drinking water purified by purifiers(in ppm), he/she takes a random sample of n = 31 and the sample mean obtained is M = 22 ppm and the sample standard deviation as s = 1 ppm.

Hence the confidence interval for a 95% confidence level is computed as:

μ = M ± t(s_M)

where:

M = sample mean

n = Sample size

df = degree of freedom = n-1
t = t statistic determined by confidence level and the degree of freedom
s_M = standard error = √(s²/n)

Assumption:

1) The sample is randoomly selected.

2) Population is normally distributed.

Since the population standard deviation is not known hence t-distribution is applicable for confidence interval calculation.

Calculation

M = 22

n= 31

df = 31-1= 30
t = 2.04 computed using the excel formula for t-distribution which is =T.INV.2T(0.05, 30)
s_M = √(2²/31) = 0.36

μ = M ± t(s_M)
μ = 22 ± 2.04*0.36
μ = 22 ± 0.73

Thus the confidence interval for population mean is computed as:

=> CI = [21.27, 22.73].