Question

1. What trends do you notice in your data set?

2.Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two tailed) would you have to complete?

3.Explain the steps needed to complete the Hypothesis Test. What is needed?

Location	Data Type	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016
New York	Number	31,187	30,061	30,229	28,124	26,302	25,759	25,378	25,398	24,656	24,073
	Percent	12%	12%	12%	12%	11%	11%	11%	11%	10%	10%

Answer 1

Solution:

Question 1

We notice that the data is uniformly distributed through the year 2007 to 2016.

Question 2

Based on the trends and history of given data, the claim is that the given data is uniformly distributed through the year 2007 to 2016.

Here, we have to use Chi square test for goodness of fit and this test is two tailed.

Question 3

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H₀: The given data is uniformly distributed through the year 2007 to 2016.

Alternative hypothesis: H_a: The given data is not uniformly distributed through the year 2007 to 2016.

We assume level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

We are given

N = 10

Degrees of freedom = df = N – 1 = 10 – 1 = 9

α = 0.05

Critical value = 16.91897762

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Year	O	E	(O - E)^2	(O - E)^2/E
2007	31187	27116.7	16567342	610.9645381
2008	30061	27116.7	8668902.5	319.688697
2009	30229	27116.7	9686411.3	357.212024
2010	28124	27116.7	1014653.3	37.41802247
2011	26302	27116.7	663736.09	24.47702302
2012	25759	27116.7	1843349.3	67.97837827
2013	25378	27116.7	3023077.7	111.4839818
2014	25398	27116.7	2953929.7	108.9339665
2015	24656	27116.7	6055044.5	223.2957731
2016	24073	27116.7	9264109.7	341.638536
Total	271167	271167		2203.09094

Chi square = ∑[(O – E)^2/E] = 2203.09094

P-value = 0.00

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is insufficient evidence to conclude that the given data is uniformly distributed through the year 2007 to 2016.