Question

An engineer wants to measure the bias in a pH meter. She uses the meter to measure the pH in 6 neutral substances and obtains pH readings of 7.08, 7.04, 7.07, 6.99, 7.10, and 7.12.

a.   Find the mean and standard deviation for the pH values (show your work).

b.   Create a 95% confidence interval for the pH values read by this meter. Use a t critical value of 2.571.

c.   Explain in context what your confidence interval tells you about the pH values read by this meter.

d.   The actual pH of the substances tested was 7. Is there evidence the pH meter is testing inaccurately?

Answer 1

a.

The sample size is n=6. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	7.08	50.1264
	7.04	49.5616
	7.07	49.9849
	6.99	48.8601
	7.10	50.41
	7.12	50.6944
Sum =	42.4	299.637

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation ss is

b.

The critical value for α=0.05 and df=n−1=5 degrees of freedom is . The corresponding confidence interval is computed as shown below:

c.

Therefore, based on the data provided, the 95% confidence interval for the population mean is 7.019<μ<7.115, which indicates that we are 95% confident that the true population mean of pH values, μ is contained by the interval (7.019,7.115).

d.

Since 7 does not lie in the above confidence interval, therefore there is enough evidence the pH meter is testing inaccurately.

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