Question

An engineer wants to measure the bias in a pH meter. She uses the meter to measure the pH in 14 neutral substances (pH=7.0) and obtains the data shown in the table.

7.01 7.04 6.97 7.00 6.99 6.97 7.04 7.04 7.01 7.00 6.99 7.04 7.07 6.97

Is there evidence to support that the pH meter is correctly calibrated? Use the α = 0.05 level of significance.

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the pH meter is correctly calibrated.

Alternative hypothesis: Ha: the pH meter is not correctly calibrated.

H0: µ = 7 versus Ha: µ ≠ 7

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 7

Xbar = 7.01

S = 0.031622777

n = 14

df = n – 1 = 13

α = 0.05

Critical value = - 2.1604 and 2.1604

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (7.01 – 7)/[ 0.031622777/sqrt(14)]

t = 1.1832

P-value = 0.2579

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the pH meter is correctly calibrated.