IMathAS-libretexts

The numbers of COVID-19 deaths among NYC residents in April 2020 are given in the following table:

Test the hypothesis that the virus affects different age groups evenly. Use 1% level of significance.

Procedure:

Assumptions: (select everything that applies)

Step 1. Hypotheses Set-Up:

\displaystyle {H}_{{0}}:

\displaystyle {H}_{{a}}:

, and the test is

Step 2. The significance level $\displaystyle \alpha=$ %

Step 3. Compute the value of the test statistic using the table below: (Round the answers to 4 decimal places)

Category	[O]bserved	[E]xpected	$\displaystyle {O}-{E}$	$\displaystyle {\left({O}-{E}\right)}^{{2}}$	$\displaystyle \frac{{\left({O}-{E}\right)}^{{2}}}{{E}}$
0-17	12		-1131.2	1279613.44	1119.326
18-44	312	1143.2		690893.44	604.3505
45-64	1561	1143.2	417.8		152.6914
65-74	1638	1143.2	494.8	244827.04
75+	2193	1143.2	1049.8	1102080.04	964.0308
Total:				$\displaystyle =\sum\frac{{\left({O}-{E}\right)}^{{2}}}{{E}}=$
				df=

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA	PVA
Provide the critical value(s) for the Rejection Region:	Compute the P-value of the test statistic:
left CV is and right CV is	P-value is

Step 5. Decision:

CVA	PVA
Is the test statistic in the rejection region?	Is the P-value less than the significance level?

Conclusion:

Step 6. Interpretation:

At 1% significance level we have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.