Answer to Question #207681 in Statistics and Probability for Janna

Question

The Coronavirus Disease is an infectious disease caused by a new strain of coronavirus. The World Health Organization claims that the incubation period of the virus in the infected person has a mean of 6.1 days. The doctors in the Philippines conducted a research and they found out that incubation period of the virus in human body is 7.03 days with a standard deviation of 4.32. The samples were 46 COVID patients. Is there enough evidence to conclude that the incubation period of the virus is 6.1 days as stated, at a=0.01?

Answer 1

$H0:\mu=6.1$

$Ha:\mu\ne6.1$

Population variance is unknown, thus, t-distribution is used.

$t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$

$t=\frac{7.03-6.1}{\frac{4.32}{\sqrt{46}}}=1.46$

$Cv=t_{0.005,45}=2.69$

Since 1.46<2.69, we fail to reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the incubation period for the virus is 6.1 days.