Final answer:
The question is about using a two-sample t-test to compare the recovery rates of COVID-19 patients across different age cohorts. A t-statistic is calculated using sample means, standard deviations, and sizes to determine if the difference between groups is statistically significant.
Step-by-step explanation:
The question pertains to conducting a hypothesis test to determine whether the recovery rate for COVID-19 patients differs by age cohort, specifically comparing 'youth' and 'adults'. To perform this test, we would typically use a two-sample t-test, which compares the means of two independent samples to see if there is a statistically significant difference between them.
To calculate the test statistic for the two-sample t-test, we use the following formula:
t = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2))
where X1 and X2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes for the two groups.
In the context of this problem, the test value (or t-statistic) would be calculated using the following values:
- Sample mean for youth: 12 days
- Sample mean for adults: 17 days
- Sample standard deviation for youth: 3 days
- Sample standard deviation for adults: 5 days
- Sample size for youth: 3650
This calculation will provide us the test statistic, which we can then compare to a critical value from the t-distribution to determine whether the difference between the two age cohorts is statistically significant.