Answer:
72.5% of the samples could be considered acid rain.
Explanation:
Hello!
You have the data of a pH of 40 samples of rainwater. The researcher considers that rain with a pH < 5.3 is acid.
To determine what percentage of the samples could be considered as acid rain, you have to first organize the raw data into a frequency table.
The pH of the rainwater is a continuous variable.
Step 1
Define the class intervals.
The number of intervals to use is up to you, considering the range of values I've chosen 6 intervals.
To determine the width of the intervals you have to calculate the range of the data set:
Range: Max value - Min value= 5.7 - 3.1 = 2.6
Now you divide it by the number of intervals you determined.
2.6/6= 0.43
Finally, you calculate the bonds of the interval starting from the lowest value
3.1+0.43= 3.53 and so on:
1) [3.1-3.53)
2) [3.53-3.96)
3) [3.96-4.39)
4) [4.39-4.82)
5) [4.82-5.25)
6) [5.25;5.7)
Step 2
Organize the data.
fi: absolute frequency, each observation that corresponds with the interval range.
hi: relative frequency ⇒ fi/n
The relative frequency is the proportion of observations of the variable.
Hi= accumulative relative frequency ⇒ ∑hi
(check attachment)
Step 3
Now that you have the data organized you can easily determine the proportion of samples that have a pH below 5.3:
P(X<5.3)
The value of X= 5.3 is included in the last interval, the proportion of observations below it is the accumulated relative frequency until the interval before last 5) [4.82-5.25)
P(X<5.3)= H(5)= 0.725
72.5% of the samples could be considered acid rain.
I hope it helps!