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 1.46 liters. A sample of 10 adults after the campaign shows the following consumption in liters:

At the .05 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value.

Compute the value of the test statistic. (Round the value of standard deviation and final answer to 3 decimal places.)

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   1.46  
Ha:    u   >   1.46   [ANSWER]

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b)
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          
tcrit =    +   1.833112933      

Thus, we Reject Ho if t > 1.833. [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    1.68          
uo = hypothesized mean =    1.46          
n = sample size =    10          
s = standard deviation =    0.21725561          
              
Thus, t = (X - uo) * sqrt(n) / s =    3.202 [ANSWER]

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d)          
              
As t > 1.833, we REJECT HO, and conclude that the water consumption has INCREASED.

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e)

Looking at a table, we see that it is BETWWEN 0.01 AND 0.005. [ANSWER]