The Environmental Protection Agency has determined that safe drinking
water should have an average pH of 7 moles per liter. You are testing water from a new source, and take 30 vials of water. Water is unsafe if it deviates too far from 7 moles per liter in either direction. The mean pH level in your sample is 6.4 moles per liter, which is slightly acidic. The standard deviation of the sample is 0.5 moles per liter.

b) A 95% confidence interval for the true mean pH level of the water is (6.21, 6.59). Interpret this interval.

c) Explain why the interval in part (b) is consistent with the result of the test in part (a).

b)

The confidence interval for this case is given (6.21, 6.59)

So we can conclude at 95% of confidence that the true mean for the PH concentration is between 6.21 and 6.59 moles per liter

c) Since the confidence interval not contains the value 7 we reject the hypothesis that the true mean is equal to 7. And the same result was obtained with the t test for the true mean.

Explanation:

We assume that part a is test the claim. And we can conduct the following hypothesis test:

Null hypothesis:

Alternative hypothesis

The statistic is to check this hypothesi is given by:

We know the following info from the problem:

Replacing we got:

And the p value would be:

Since the p value is very low compared to the significance assumed of 0.05 we have enough evidence to reject the null hypothesis that the true mean is equal to 7 moles/liter

Part b

The confidence interval is given by:

The confidence interval for this case is given (6.21, 6.59)

So we can conclude at 95% of confidence that the true mean for the PH concentration is between 6.21 and 6.59 moles per liter

Part c

Since the confidence interval not contains the value 7 we reject the hypothesis that the true mean is equal to 7. And the same result was obtained with the t test for the true mean.