IMathAS-libretexts

Government regulations require a certain industrial plant to discharge no more than 1000 gallons of wastewater per hour, on average, into a nearby lake. An environmental organization suspects the plant discharges more, and tests this suspicion by randomly sampling the discharge at ten different hours over a period of a week. The readings (in gallons of waste water) are shown below. Test the environmental organization's suspicion at that 5% significance level.

1116	1190	1080	1000	1149
907	916	1060	1344	1323

(a) Write the hypotheses in symbols.

H₀: μ = 1000
H_a: μ > 1000
H₀: μ = 1000
H_a: μ ≠ 1000
H₀: μ = 1000
H_a: μ < 1000
H₀: μ ≠ 1000
H_a: μ = 1000
H₀: μ < 1000
H_a: μ = 1000

(b) Use appropriate technology to compute the sample mean and sample standard deviation:

Sample mean: (Please round to the nearest whole number.)
Sample standard deviation: (Please round to the nearest whole number.)

(c) Compute the standard error (for samples of size 10) and the test statistic T.

Standard error = (Please round to one decimal places.)

T = (Please round to two decimal places.)

(d) Find and interpret the P-value in this context. Drawing a picture may be helpful. (Round to four decimal places.)
The P-value is

(e) What is the conclusion of the hypothesis test? (Recall that the significance level α is 0.05.)

Since the P-value is not small, we do not have enough evidence to reject the null hypothesis.
Since the P-value is small, we reject the null hypothesis and accept the alternative.
Since the P-value is not small, we accept the null hypothesis.
Since the P-value is not small, we reject the null hypothesis and accept the alternative.
Since the P-value is small, we fail to reject the null hypothesis.

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