The amount of water consumed each day by a healthy adult follows a normal distri

Question

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 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: At the .01 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. a. State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.) b. State the decision rule for .01 significance level. (Round your answer to 3 decimal places.) c. Compute the value of the test statistic. (Round your intermediate and final answer to 3 decimal places.) d. At the .01 level, can we conclude that water consumption has increased? e. Estimate the p-value.

Explanation / Answer

Given that,
population mean(u)=1.4
sample mean, x =1.6
standard deviation, s =0.216
number (n)=10
null, Ho: <=1.4
alternate, H1: >1.4
level of significance, = 0.01
from standard normal table,right tailed t /2 =2.821
since our test is right-tailed
reject Ho, if to > 2.821
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.6-1.4/(0.216/sqrt(10))
to =2.928
| to | =2.928
critical value
the value of |t | with n-1 = 9 d.f is 2.821
we got |to| =2.928 & | t | =2.821
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.928 ) = 0.00841
hence value of p0.01 > 0.00841,here we reject Ho
ANSWERS
---------------
null, Ho: <=1.4
alternate, H1: >1.4
test statistic: 2.928
critical value: 2.821
decision: reject Ho
p-value: 0.00841

we have evidence that consum[ption has increased

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