In a certain chemical process, it is very important that a particular solution t
ID: 3780305 • Letter: I
Question
In a certain chemical process, it is very important that a particular solution that is to be used as a reactant have a pH of exactly 8.20. A method for determining pH that is available for solutions of this type is known to give measurements that are normally distributed with a mean equal to the actual pH and with a standard deviation of .02. Suppose 10 independent measurements yielded the following pH values: 8.18 8.17 8.16 8.15 8.17 8.21 8.22 8.16 8.19 8.18 a) What conclusion can be drawn at the alpha_1 = .10 level of significance? b) What about at the alpha_2 = .05 level of significance? c) What is the p-value?Explanation / Answer
a) Mean of these values = 8.179
STD of these values = 0.0211896201004
a = 0.1
Assuming two tailed test.
Test statistic = (8.179-8.2)/(std/sqrt(n))
Test statistic = (8.179-8.2)/(0.0211896201004/sqrt(10)) =
-3.13397930444
critical value = 1.833 from t table
Since, -3.1339 is less than -1.833, we can reject the null hypothesis.
b) Mean of these values = 8.179
STD of these values = 0.0211896201004
a = 0.1
Assuming two tailed test.
Test statistic = (8.179-8.2)/(std/sqrt(n))
Test statistic = (8.179-8.2)/(0.0211896201004/sqrt(10)) =
-3.13397930444
critical value = 2.262 from t table
Since, -3.1339 is less than -1.833, we can reject the null hypothesis.
c) Similarly, P-value from the t table, is approximately 0.02.