Question

Exhibit Symptom of COVID-19

Study shows that about 70% of the COVID-19 patients have a dry cough (which does not bring up any mucus or phlegm). To use hypothesis testing method to check the credibility of this study, you randomly surveyed 25 patients of COVID-19 and 18 of them answered that they are having dry cough.

1. Refer to Exhibit Symptom of COVID-19. What is the value of the test statistics?

2. Refer to Exhibit Symptom of COVID-19. Which of the followings CAN be used to calculate the answer in Question 6? (Select ALL that apply.)

-2*(1 - NORM.DIST( sample proportion, 0.7, std. dev. of population, 1 ))

-2*(1 - NORM.DIST( 18/25, 0.7, sqrt(0.7*0.3/25), 1 ))

-T.DIST.2T( t-test, 24)

-2*T.DIST.RT( (18/25 - 0.7)/(sqrt(0.7*0.3/25)), 24 )

-1 - BINOM.DIST.RANGE(25, 0.7, 25*0.7-0.5, 25*0.7+0.5)

-2*(1 - NORM.DIST( z-test, 0, 1, 1) )

-2*NORM.S.DIST( z-test, 1)

-2*NORM.DIST( 18/25, 0.7, sqrt(0.7*0.3/25), 1 )

-2*(1 - NORM.S.DIST( z-test, 1))

3. In this question, the symbol "<=" means "", and ">=" means "".

Suppose you the significance level you have chosen is α=0.09. This corresponds to a critical value to be  [ Select ] . Hence, you will  [ Select ] the null hypothesis H0. And conclude that, from this sample of 25 patients, there is  [ Select ] to say that the population proportion of dry cough symptom is  [ Select ] . This is because the p-value is  [ Select ] the α value, and the relationship between the test statistic and the critical value is  [ Select ] .

Answer 1

Suppose the significance level we have chosen is α=0.09. This corresponds to a critical value to be -1.6854 or 1.6954. Hence, you will Fail to reject the null hypothesis H0. And conclude that, from this sample of 25 patients, there is enough evidence to say that the population proportion of dry cough symptom is 0.70 . This is because the p-value is greater than α value, and the relationship between the test statistic and the critical value is more.