Question: 11-4. This year’s water pollution readings at State Park Beach seem to

Question

Question:

11-4. This year’s water pollution readings at State Park Beach seem to be lower than last year. A sample of 30 readings was randomly selected from this year’s daily readings:

Researchers want to know if this is sufficient evidence to conclude that the mean of this year’s pollution readings is significantly lower than last year’s mean of 3.8. What is the t-score or t-stat?

Explanation / Answer

t score = [mean(all sample readings) - mean(population)] / square_root[variance(all sample readings) / total number of samples]

t score = (3.663333 - 3.8) / square_root( 0.0265 / 30 ) = -4.5948 (Answer)

Take all the sample values in R by typing:

y=c(3.6,3.9,3.3,3.4,3.8,3.7,3.5,3.6,3.7,3.6,3.6,3.7,3.9,3.8,3.7,4.0,3.7,3.5,3.8,3.6,3.5,3.6,3.5,3.7,3.6,3.9,3.9,3.7,3.6,3.5)

'y' is a vector containing all the sample readings.

to calculate t-test score, apply this function:
t.test(a,mu = 3.8)

output :

One Sample t-test

data: y
t = -4.5948, df = 29, p-value = 7.81e-05
alternative hypothesis: true mean is not equal to 3.8
95 percent confidence interval:
lower and upper bound of population mean obtained =>(3.602501,3.724166) [therefore, by the upper bound it shows that population mean
sample estimates: mean of x : 3.663333

Answer :

t = -4.5948

and

lower and upper bound of population mean obtained =>(3.602501,3.724166) [therefore, by the upper bound it shows that approximate population mean is about 3.74166 i.e. less than 3.8 i.e. last year's mean].

Therefore, we have sufficient evidence to conclude that the mean of this year’s pollution readings is significantly lower than last year’s mean of 3.8

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