Question

Do you drink the recommended amount of water each day? Most Americans don't! On average, Americans drink 5.3 eight-oz servings of water a day. A sample of 37 education professionals was randomly selected and their water consumption for a 24-hour period was monitored; the mean amount consumed was 44.2 oz. Assuming the amount of water consumed daily by adults is normally distributed and the standard deviation is 10.8 oz, is there sufficient evidence to show that education professionals consume, on average, more water daily than the national average? Use α = .05.

(a) Find z. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Reject the null hypothesis, there is significant evidence that education professionals consume more water daily.

Fail to reject the null hypothesis, there is significant evidence that education professionals consume more water daily.   

Reject the null hypothesis, there is not significant evidence that education professionals consume more water daily.

Fail to reject the null hypothesis, there is not significant evidence that education professionals consume more water daily.

Answer 1

Sample size = n = 37

Sample mean = = 44.2

Population standard deviation = = 10.8

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

P-value = P(Z > 1.01) = 0.1553

P-value > 0.05 we fail to reject the null hypothesis.

Conclusion:Fail to reject the null hypothesis, there is not significant evidence that education professionals consume more water daily.