Question

According to an English professor, the following information represents the percent of times that each letter is used in the English language:

E = 11.16%, A = 8.5%, I = 7.54%, O = 7.16%, U = 3.63% (E.g. 11.16% of letters found in any writing sample will be letter E's)

Choose a paragraph of at least 30 words from any written source and count the number of times each vowel shows up in your paragraph. Then, perform a goodness-of-fit test to see if the above percents are a good fit for the population based on your sample paragraph.

Please make sure you include your paragraph when you submit your assignment. Note spaces, apostrophe's, etc. do not count towards the total number of letters in your paragraph.

Paragraph:

The Centers for Disease Control and Prevention have advised people to “put distance” between themselves and others if the virus is spreading in their community. Thousands of Americans are following this directive, and numerous workplaces have directed their employees to work from home.

Answer 1

From the given paragraph we calculate appearance of each of the vowels as well as total number of letters.

Total number of letters = 239

So, expected and observed frequencies are as follows.

Vowel	Observed frequency (Oi)	Expected frequency (Ei)	(Oi-Ei)2/Ei
A	14	239*8.5/100=20.3150	1.963043
E	36	239*11.16/100=26.6724	3.261953
I	18	239*7.54/100=18.0206	0.000024
O	19	239*7.16/100=17.1124	0.208214
U	6	239*3.63/100= 8.6757	0.825221
Total	93	90.7961	6.258455

We have to perform chi square test for goodness of fit.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistics is given by

Here,

Number of observations

Degrees of freedom

Corresponding

We found p-value significantly higher. So we can take our null hypothesis.

Hence based on our sample paragraph, at 82% (and more) confidence interval we can conclude that the given percents are a good fit for the population.