Question

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.28 liters. A sample of 10 adults after the campaign shows the following consumption in liters:

   1.90   1.62   1.78   1.30   1.68   1.46   1.46   1.66   1.32   1.52

At the .10 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.)

H0: μ ≤
H1: μ >

(b)	State the decision rule for .10 significance level. (Round your answer to 3 decimal places.)

Reject H0 if t >

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

Value of the test statistic

(d)	At the .10 level, can we conclude that water consumption has increased?

  (Click to select)RejectFail to reject H₀. and conclude that water consumption has (Click to select)increasednot increased.

(e)	Estimate the p-value.

p-value

(Click to select)less than 0.0005between 0.005 and 0.0005between 0.005 and 0.1greater than 0.005

Answer 1

a)

null hypothesis: Ho:             μ		<=	1.28
Alternate Hypothesis: Ha:μ		>	1.28

b)

Decision rule :                   reject Ho if test statistic t>1.383

c)

population mean μ=	1.28
sample mean         x=	1.570
sample size             n=	10.00
sample std deviation s=	0.194
std error sx=s/√n=	0.0613
test stat t='(x-μ)*√n/s=	4.734

d)

Reject Ho , and conclude that water consumption has  

increased.

e)

between 0.005 and 0.0005