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χ² Goodness-of-Fit Test

In a combined Stat 100 and Stat 200 survey in Fall 2017, one question asked was "What month were you born in?". The data can be downloaded here and then loaded to R using the command

f17 <- read.csv("stat100_200_2017fall_survey04.csv")

A description of the column variables can be found on this webpage. Explore the data.

We want to test the following hypothesis:

H₀: Students in Stat 100 and Stat 200 were born with equal probability in each month.

Assuming H₀, what is the expected proportion of students born in each month? Round your answer to 3 decimal places.

Expected proportion =

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Now look at the survey data. What are the largest and smallest proportion of students born in the 12 months? Which months have the largest and smallest proportion?

Largest proportion = (round to 3 decimal places) in

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Smallest proportion = (round to 3 decimal places) in

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Perform a χ² goodness-of-fit test. Calculate the p-value [i.e. P(χ² > observed χ² | H₀)]. Then use it to determine if the data is consistent with the hypothesis H₀ at the 5% significance level.

p-value = (round to 3 decimal places)

Reject H₀ at 5% significance level?
Yes, reject H₀: There is a significant evidence to suggest that students were not born with equal probability in each month.
No, do not reject H₀: There is no/not enough evidence to suggest that students were not born with equal probability in each month.

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The next two parts of the problem will show up after you finish parts (a)-(c).