Question

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.32 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: 1.35 1.42 1.34 1.42 1.44 1.64 1.90 1.64 1.50 1.38 At the 0.025 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value.

State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.) State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Round your intermediate and final answer to 3 decimal places.) At the 0.025 level, can we conclude that water consumption has increased? Estimate the p-value.

Answer 1

	Values ( X )
	1.35	0.0234
	1.42	0.0069
	1.34	0.0266
	1.42	0.0069
	1.44	0.004
	1.64	0.0188
	1.9	0.1576
	1.64	0.0188
	1.5	0
	1.38	0.0151
Total	15.03	0.2781

Mean

Standard deviation

Sample variance = 0.0309

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 3.2918

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

P value = P ( t > 3.2918 ) = 0.0047

reject null hypothesis if P value < level of significance

P value = 0.0047 < 0.025, hence we reject null hypothesis

Conclusion :- There is sufficient evidence to support the claim that water consumption has increased.