Question

7. A student measures the mass percent chloride in their unknown four times by each of two methods. (a) Find the mean, standard deviation, and 95% confidence limit for each method. (b) Determine if each method’s result is “significantly” different from the expected value of 48.86% Chloride. (c) Use the F test to decide whether the standard deviations are “significantly” different. (d) Use the t test to decide whether the means are different from one another at the 95% confidence level.

Method Replicate Measurements

A 47.62% 47.91% 47.83% 47.79% 48.01%

B 47.11% 49.63% 48.72% 49.17% 47.99%

Answer 1

a)

A	B
47.62	47.11
47.91	49.63
47.83	48.72
47.79	49.17
48.01	47.99
47.832	48.524	mean
0.145327	0.99543	sd

Formulas

A	B
47.62	47.11
47.91	49.63
47.83	48.72
47.79	49.17
48.01	47.99
=AVERAGE(A2:A6)	=AVERAGE(B2:B6)	mean
=STDEV(A2:A6)	=STDEV(B2:B6)	sd

for alpha =0.05 , df =n-1 = 4

critical value = 2.776

for A

lower	47.6516
upper	48.0124

for B

lower	47.2880
upper	49.7600

b)

for A

	CI
	xbar	47.83
	sd	0.15
	n	5
	mu	48.86
	alpha	0.05
	TS	-15.82
p-value
	2-tailed	0.0001

p-value = 0.0001 < alpha

hence we reject the null hypothesis

we conclude that A is significantly different from 48.86%

for B

	CI
	xbar	48.52
	sd	1.00
	n	5
	mu	48.86
	alpha	0.05
	TS	-0.75
p-value
	2-tailed	0.4924

p-value = 0.4924 > alpha

hence we fail to reject the null hypothesis

c)

d)

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