Question

Data on the pH of rain in Ingham County, Michigan, are as follows: 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 What proportion of the samples has pH below 5.0?

Answer 1

Answer:

$\hat p =\frac{26}{39}=0.667$

Step-by-step explanation:

Some important concepts

A proportion refers to "the fraction of the total that possesses a certain attribute"

The data det ordered from the smallest to the largest value is:

3.1 ,3.71 ,3.71 ,3.74 ,3.98 ,3.98 ,4.15 ,4.16 ,4.16 ,4.32 ,4.34 ,4.51 ,4.51 ,4.56 ,4.57 ,4.57 ,4.57 ,4.61 ,4.62 ,4.63 ,4.64 ,4.64 ,4.64 ,4.64 ,4.86 ,4.96 ,5.04 ,5.11 ,5.12 ,5.37 ,5.37 ,5.38 ,5.39 ,5.47 ,5.48 ,5.62, 5.65 ,5.65 ,5.7

If we are interesed on the sample values below 5.0 we need to count how many values are below this number. If we do this we got that 26 numbers are below 5.0 and the total of numbers are 39.

so the proportion on this case would be"

$\hat p =\frac{26}{39}=0.667$