Question

An industrial company claims that the mean pH level of the water in nearby river is 6.8. A water sample of n = 9, when tested, yields a sample mean pH level of 6.7. If the distribution of pH level of water is normally distributed with a standard deviation σ = 0.24. Is there enough evidence to support the company’s claim at a significance level α = 0.05? Conduct a two-tailed test. (5 points) State your approach (either the p-value or critical value approach): Step 1. State the null and alternative hypotheses. Step 2. Select the distribution to use. Step 3. Calculate the p-value. Step 4. Make a decision, and state your conclusion with statistical evidence.

Answer 1

Step 1) Null hypothesis H0 : = 6.8

Alternative hypothesis H1 : 6.8

Step 2) Here sample from normal distribution and population standard deviation is known , so we use standard normal distribdistribution

The test statistic Z is

Z = (xbar - ) /(/√n)

Z =( 6.7 - 6.8)/(0.24/√9)

Z = -1.25

Step 3) P value for Z = -1.25 and two tailed test

p value = 2 * P( Z < -1.25)  

Using z table P( Z< -1.25) = 0.1056

p-value = 0.2113

step 4) Decision rule : If p-value    , we reject null hypothesis H0 otherwise we fail to reject the null hypothesis H0

Here = 0.05 , so p-value =0.2113 > 0.05

Decision : we fail to reject the null hypothesis H0.

Conclusion: There is sufficient evidence to support the companys claim .