Question

Two types of solutions, A and B, were tested for their pH (degree of acidity of the solution). Analysis of 6 samples of A showed a mean pH of 6.72 with a standard deviation of 0.024. Analysis of 5 samples of B showed a mean pH of 6.49 with a standard deviation of 0.032. Using a 0.05 significance level, determine whether the two types of solutions have different pH values.

Answer 1

Solution:

Given:

Type A solution:

Sample size = n₁ = 6

Sample mean pH =

Sample standard deviation = s₁ = 0.024

Type B solution:

Sample size = n₂ = 6

Sample mean pH =

Sample standard deviation = s₂ = 0.032

Significance level = 0.05

We have to test whether the two types of solutions have different pH values.

Step 1) State H0 and H1:

Vs

Step 2) Find test statistic value:

where

Thus

Step 3) t critical values:

df = n1 + n2 - 2 = 6 +5 - 2 = 9

Since this is two tailed test, we look for two tail area= Significance level = 0.05

t critical values = ( -2.262 , 2.262 )

Step 4) Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value = 2.262, otherwise we fail to reject H0

Since t test statistic value = > t critical value = 2.262, we reject null hypothesis H0.

Step 5) Conclusion:

At  0.05 significance level, we have sufficient evidence to conclude that the two types of solutions have different pH values.