Question

Industrial wastes and sewage dumped into our rivers and streams absorb oxygen and thereby reduce the amount of dissolved oxygen available for fish and other forms of aquatic life. One state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. A pollution control inspector suspected that a river community was releasing amounts of semitreated sewage into a river. To check his theory, he drew five randomly selected specimens of river water at a location above the town, and another five below. The dissolved oxygen readings (in parts per million) are as follows.

Above Town	4.9	5.3	4.9	4.9	5.1
Below Town	5.1	4.6	4.8	4.9	4.9

(a) Do the data provide sufficient evidence to indicate that the mean oxygen content below the town is less than the mean oxygen content above? Test using α = 0.05. (Use μ₁ for the population mean for the above town location and μ₂ for the population mean for the below town location.)
State the null and alternative hypotheses.

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) > 0

State the test statistic. (Round your answer to three decimal places.)
t =  

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t >

t <

State the conclusion.

H₀ is rejected. There is insufficient evidence to indicate that the mean content of oxygen below town is less than the mean content above town.

H₀ is not rejected. There is sufficient evidence to indicate that the mean content of oxygen below town is less than the mean content above town.    

H₀ is not rejected. There is insufficient evidence to indicate that the mean content of oxygen below town is less than the mean content above town.

H₀ is rejected. There is sufficient evidence to indicate that the mean content of oxygen below town is less than the mean content above town.

(b) Suppose you prefer estimation as a method of inference. Estimate the difference in the mean dissolved oxygen contents (in ppm) for locations above and below the town. Use a 95% confidence interval. (Use μ₁ − μ₂. Round your answers to three decimal places.)
ppm to  ppm

Answer 1

	Above ( X )		Below ( Y )
	4.9	0.0144	5.1	0.0576
	5.3	0.0784	4.6	0.0676
	4.9	0.0144	4.8	0.0036
	4.9	0.0144	4.9	0.0016
	5.1	0.0064	4.9	0.0016
Total	25.1	0.128	24.3	0.132

To Test :-

H₀ :-  

H₁ :-  

Test Statistic :-

Test Criteria :-

Reject null hypothesis if

Critical value

Rejection region t > 1.895

Result :- Fail to Reject Null Hypothesis

Conclusion :- Accept Null Hypotesis

There is no sufficient evidence to suppport the claim that  the mean oxygen content below the town is less than the mean oxygen content above.

H0 is not rejected. There is insufficient evidence to indicate that the mean content of oxygen below town is less than the mean content above town.

Part b)

Confidence interval :-

95%  Confidence interval is ( -0.139 , 0.459 )