# Mean

The mean amount of water consumed each day by a healthy adult is 1.4 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign shows the following consumption in liters:

1.4, 1.6, 1.5, 6.4, 1.9, 0.4, 1.3, 1.9, 1.8, 1.7

(a)    Generate a summary statistics of the data using descriptive statistics of Excel Data Analysis tool. Do you observe any unusual observation? If the answer is yes, how would you handle that observation? Justify your answer. [ Hint: you may construct a box plot to identify any unusual observation. If an unusual observation is found, you may include it to your analysis or you may discard it from your analysis. Whatever you decide, write one paragraph to justify it.]

Can we conclude that water consumption has increased? Perform the following tests to answer this question (for questions b, d and e: state the hypotheses, find out critical/table value, find out the value of the test statistic, and write conclusion)  –

(b)   Use a suitable parametric procedure. State any assumption that you make. Use α=.05. Calculate P-value.  [Hint: Perform one sample t test, discussed in chapter 9. H0: µ=1.4, Ha: µ>1.4 ]

(c)    Check the model assumption stated in your answers for part (b). [Hint: Construct a normal probability plot of the sample data using Excel. Place X at the horizontal axis and z-score at the vertical axis.]

(d)   Use Sign test with α close to .05. Make sure to write conclusion using P-value.

(e)    Which method would you recommend for this example? Why?

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