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Answer:
The mean water hardness of lakes in Kansas is 425 mg/L or greater.
Step-by-step explanation:
We are given the following data set:
346, 496, 352, 378, 315, 420, 485, 446, 479, 422, 494, 289, 436, 516, 615, 491, 360, 385, 500, 558, 381, 303, 434, 562, 496
Formula:
where are data points,
is the mean and n is the number of observations.
Sum of squares of differences = 175413.76
Population mean, μ = 425 mg/L
Sample mean, = 438.36
Sample size, n = 25
Alpha, α = 0.05
Sample standard deviation, s = 85.49
First, we design the null and the alternate hypothesis
We use one-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
The calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis and accept it.
Thus, the mean water hardness of lakes in Kansas is 425 mg/L or greater.