Question

The Environmental Protection Agency has determined that safe drinking

Answer 1

Answer:

b) $\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$

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: $\mu =7$

Alternative hypothesis $\mu \neq 7$

The statistic is to check this hypothesi is given by:

$t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}$

We know the following info from the problem:

$\bar X = 6.4 , s=0.5, n =30$

Replacing we got:

$t = \frac{6.4-7}{\frac{0.5}{\sqrt{30}}}= -6.573$

And the p value would be:

$p_v= 2*P(Z$

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:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$

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.