Question

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.50 liters. A sample of 10 adults after the campaign shows the following consumption in liters:

1.52 1.64 1.66 1.40 1.82 1.70 1.90 1.45 1.78 1.92

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.)

H0: μ ≤ ?

H1: μ > ?

(b) State the decision rule for .01 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 .01 level, can we conclude that water consumption has increased?

(reject or do not reject) H0. and conclude that water consumption has (increased or not increased).

(e) Estimate the p-value.

p-value:

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ <= 1.5
Alternative Hypothesis, Ha: μ > 1.5

b)

Rejection Region
This is right tailed test, for α = 0.01 and df = 9
Critical value of t is 2.821.
Hence reject H0 if t > 2.821

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.677 - 1.5)/(0.183/sqrt(10))
t = 3.059

d)

(reject ) H0. and conclude that water consumption has (increased ).

e)

P-value = 0.0068