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. A health campaign promotes the consumption of at least 2.0 liters per day:

   1.90   1.62   1.78   1.30   1.68   1.46   1.46   1.66   1.32   1.52

At the 0.100 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 0.100 significance level. (Round your answer to 3 decimal places.)

Reject H0 if t >

________

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

Value of the test statistic

__________

d.	At the 0.100 level, can we conclude that water consumption has increased?

Fail to reject or Reject H₀

Conclude that water consumption has

Increased or not increased.

e.	Estimate the p-value.

p-value is: greater than 0.10 between 0.025 and 0.05 less than 0.0005 between 0.01 and 0.025 between 0.005 and 0.01 between 0.05 and 0.10 between 0.0005 and 0.005

Answer 1

a)Ho: mu = muo= 1.28 V/s H1: mu <muo= 1.28

Ho : The water consumption has not increased.

H1: The water consumption has increased.

b) The 10% level of significance.

c) To .the test statistics is given by

tn-1 = (X_​bar-  ​​​​​- muo)/S/√n

_{X bar = 15.7/10 = 1.57}

_{S^2 = ( sum (X)^2 - n * (Xbar)^2 / n-1)}

_{= (24.9868). - 10*(1.57)^2 / 10-1}

_{= 24.9868- 24.649 / 9}

_{= 0.3378/9}

_{= 0.03753}

_{S= 0.03753}

_{t9 = ( 1.57- 1.28) / 0.1937/√10}

_{= 4.7344. ( Calculated value)}

_{Tabulated value t9,0.10 = 1.833}

_{Calculated value > Tabulated value}

_{Therefore we reject null hypothesis Ho.}

_{d) Conclusion: The water consumption has may be increased.}

_{e) p value = P( t9 < 4.7344) = 0.0000011226}

_{alpha = 0.10}

_{pvalue < alpha}

_{ie we reject Ho . The water consumption may be increased.}