Answer to Question #180454 in Statistics and Probability for Angela Marie Marquez

Question

The Coronavirus Disease (COVID-19) is an infectious disease caused by a new strain of

coronavirus. The World Health Organization (WHO) claims that the incubation period of the virus

in the infected person has a mean of 5.1 days. The doctors in the Philippines conducted a

research and they found out that incubation period of the virus in human body is 6.03 days with a

standard deviation of 3.32. The samples were 46 COVID patients. Is there enough evidence to

conclude that the incubation period of the virus is 5.1 days as stated, at α = 0. 01?

Prove the claim using this graphic organizer.

Given:

State the null  and alternative  hypothesis

Determine the  test statistics,  compute its  

value

Find the critical  value and draw  the critical  

region. 

(Draw the  

figure)

Draw  

conclusion

Answer 1

Let Null hypothesis

$H_o:\mu=\mu_1$ ,There is enough evidence to conclude that the incubation period of the virus is 5.1 days as stated

Alternate hypothesis

$H_1:\mu\neq \mu_1$

Here, sample mean and standard deviation is-

$\mu=5.1 days\\ \sigma=3.32$

X=6.03

n=46

We are going to perform t-test-

$t=\dfrac{(X-\mu)\sqrt{n}}{\sigma}$ $=\dfrac{(6.03-5.1)\sqrt{46}}{3.32}=1.899$

Critical value at $\alpha$ =0.01 is 2.704.

As the calculated value of t is less than the critical value so Null hypothesis is accepted, i.e. ,There is enough evidence to conclude that the incubation period of the virus is 5.1 days as stated

The critical region is-