The amount of water consumed each day by a healthy adult fol

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.36 liters. A sample of 10 adults after the campaign shows the following consumption in liters. At the 10 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. State the null hypothesis and the alternate hypothesis. State the decision rule for 10 significance level Compute the value of the test statistic At the 10 level can we conclude that water consumption has increased? Estimate the p-value

Solution

(a) Ho: mu<=1.36

H1: mu>1.36

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(b) The degree of freedom =n-1=10-1=9

It is a right-tailed test.

Given a=0.1, the critical value is t(0.1, df=9) =1.383 (from student t table)

Reject Ho if t>1.383

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(c) sample mean=1.528

sample standard deviation =0.119703

The test statistic is

t=(xbar-mu)/(s/vn)

=(1.528-1.36)/(0.119703/sqrt(10))

=4.438

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(d) Reject Ho and conclude that water consumption has increased

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(e) The p-value= P(t with df=9 >4.438) = 0.0008 (from student t table)