Question

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.56 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:

1.88	1.74	1.98	1.70	1.86	1.72	1.74	1.98	1.68	1.50

At the 0.025 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value.

1. State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)

2. State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places.)

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

4. At the 0.025 level, can we conclude that water consumption has increased?

5. Estimate the p-value.

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1.56
Alternative Hypothesis, Ha: μ > 1.56

b)
Rejection Region
This is right tailed test, for α = 0.025 and df = 9
Critical value of t is 2.262.
Hence reject H0 if t > 2.262

c)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.778 - 1.56)/(0.1483/sqrt(10))
t = 4.649

d)
Reject the null hypothesis
Sufficient evidence to conclude that the consumption has increased.

e)
P-value Approach
P-value = 0.001
p-value < 0.01