Question

In an attempt to measure the effects of acid rain, researchers measured the pH (7 is neutral and values below 7 are acidic) of water collected from rain in Ingham County, Michigan. 5.47 5.37 5.38 4.63 5.37 3.74 3.71 4.96 4.64 5.11 5.65 5.39 4.16 5.62 4.57 4.64 5.48 4.57 4.57 4.51 4.86 4.56 4.61 4.32 3.98 5.70 4.15 3.98 5.65 3.10 5.04 4.62 4.51 4.34 4.16 4.64 5.12 3.71 4.64 5.59 Many scientists consider rain with pH below 5.3 to be acid rain. What percentage of these samples could be consider as acid rain?

Answer 1

Answer:

72.5% of the samples could be considered acid rain.

Step-by-step 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!