Data Description: In this section you should describe What data is relevant for your problem Why that data supports an answer for your hypothesis How the data was collected (this should be a detailed description) Summary (descriptive) statistics including, but not limited to o Means o Variances o Proportions o r x c tables o Appropriate graphs and visualizations Analysis and Results: This section should include a description of the statistical methods that will be used in the data analysis. You should include a description of The analysis method in general, Why it is appropriate for the data you collected, The assumptions your analysis is based on. The next part is to present the results of the analysis. Include a brief description of the results (which items are "statistically significant"?) Discussion: This is where the real statistical inference is done, and where your real conclusions are made. This section should discuss how the results generalize to the population you have considered. Make sure that the population has been clearly defined and that you are careful to only generalize to the population that has been sampled. You should tell me what impact the results of your study may have. I hope this is the real meat of your project. The other parts are only there to support this section.

Here is the data:

Israeli data: How can vaccine efficacy vs. severe disease be strong when 60% of hospitalized are vaccinated?

The recent surge involving the rapidly transmitting Delta variant in heavily vaccinated countries has led to much hand-wringing that the vaccines are not effective against Delta, or vaccine effectiveness wanes after 4-6 months. In addition, in countries such as Israel with high vaccination rates, the number of "break through cases" (cases in vaccinated individuals) may outnumber the number of cases in unvaccinated peoplealthough the rates of infection and hospitalization remain much higher in unvaccinated people. However, analyses looking solely at unadjusted counts has fueled anti-vaccine sentiment suggesting the vaccines are not working and causing much stress in vaccinated people that they are not as protected as they thought they would be.

The data below were downloaded from the Israeli Ministry of Health Dashboard on August 15, 2021. The data contain the counts for hospitalizations and serious hospitalizations for covid-19 cases by age and vaccination status. This data includes only Israeli residents age 12 and older who were fully vaccinated or completely unvaccinated.

Vaccination Proportion Hospitalizations (counts) Hospitalizations (per 100k) Severe hospitalizations (count) Severe Hospitalizations (per 100k) age group % not vaccinated % vaccinated Not vaccinated Vaccinated Not vaccinated Vaccinated Not vaccinated Vaccinated Not vaccinated Vaccinated

age group	not vax	vax	partial vax	not vax per 100k	vax per 100k	partial vax 100k	severe unvax	severe vax	severe partial vax	severe unvax per 100k	risk severe 20-29	severe vax 100k	severe parital vax per 1`00k
12-15	3083	172	363	803.6	93.2	726.2	1	0	0	0.30	0.05	0.00	0.00
16-19	954	1710	85	746.8	398.5	318.8	2	0	0	1.60	0.26	0.00	0.00
20-29	1805	5308	154	678.9	535.4	357.6	4	0	0	1.50	0.24	0.00	0.00
30-39	1658	5565	127	853.7	574.4	374.5	12	2	0	6.20	1.00	0.20	0.00
40-49	1147	5465	66	789.1	589.4	253.6	24	9	1	16.50	2.66	1.00	3.80
50-59	721	4012	47	852.8	536.4	269.0	34	22	0	40.20	6.48	2.90	0.00
60-69	455	3037	19	697.8	456.2	178.1	50	58	3	76.70	12.37	8.70	28.10
70-79	237	1966	22	1155.4	423.4	373.8	39	92	2	190.10	30.66	19.80	34.00
80-89	140	994	11	1103.8	475.8	280.3	32	100	2	252.30	40.69	47.90	51.00
90+	61	264	7	1947.6	566.5	396.8	16	18	2	510.90	82.40	38.60	113.40

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