3. The recommended amount of water a person should drink is eight 8-oz servings

Question

3. The recommended amount of water a person should drink is eight 8-oz servings per day. Does the sample of education professionals in the previous page show sufficient evidence that the education professionals consume, on average, significantly less water daily than the recommended amount? Use = 0.05. See Problem 8.164 of our textbook.

The standard deviation is 11.2oz

(a) Set up the null and the alternative hypotheses.

(b) Draw the normal picture and mark the critical value x2.

(c) Find the critical value x2.

(d) Compare the critical value x2 with the observed mean ¯x to get the final conclusion.

Edit: Here is the previous question with the values that my question needs. Please do not answer this one, just use the values to answer the above

Edit 2: Eight 8oz means Quantity 8 bottles of water which are volume 8oz each

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: < 39.3

Alternative hypothesis: > 39.3

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.73

DF = n - 1 = 42 - 1

D.F = 41

t = (x - ) / SE

t = - 1.45

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 1.45. We use the t Distribution Calculator to find P(t < - 1.45) = 0.077

Thus the P-value in this analysis is 0.077

Interpret results. Since the P-value (0.077) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the educational proffesionals consume on average more water than the national average.

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