Question

During a screening experiment, a researcher recorded silica determinations (parts per million of silicon dioxide) on five filtered solutions with the following results : 229, 255, 280, 203, and 229.

a. Estimate the mean amount of silicon dioxide present in the solutiond and find a 95% confidence interval for the population mean, μ (by assuming approximate normal distribution).

b. Would you reject H0: μ = 250 vs Ha: μ ≠ 250 at α = 0.05 by using the 95% confidence interval found in part (a). Why?

Answer 1

(a)

Assumption: The distribution of silica determinations (parts per million of silicon dioxide) is normally distributed.

First we need to find the mean and standard deviation of given sample. Following is the output of descriptive statistics:

Descriptive statistics
	silica determinations, X
count	5
mean	239.20
sample standard deviation	29.30
sample variance	858.20
minimum	203
maximum	280
range	77

So we have

Degree of freedom:

df=n-1=4

The critical value for 95% confidence interval is: 2.776

The  confidence interval is:

(b)

Since confidence interval contains 250 so we fail to reject the null hypothesis at 95% confidence level.