An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 goril

Question

An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in seven home ranges in the Congo. To study the spread of the virus, researchers measure “distance” by the number of home ranges separating a group of gorillas from the first group infected.

Here are data on distance and number of days until deaths began in each later group:

Refer to above, which gives data on the distance of gorilla groups from the origin of an Ebola outbreak and the number of days until deaths from Ebola began. Software tells us that the least-squares slope is b = 11.263 with standard error SEb = 1.591.

a)Perform a hypothesis test to address whether Distance has a significant positive linear impact on Days. Define the hypotheses with the right notation.

b)Perform a hypothesis test to address whether Distance and Days are linearly correlated. Define the hypotheses with the right notation.

show your work and do not use a statistical software.

Explanation / Answer

Part-a

Null hypothesis H0:=0 is to be tested against the alternative Ha: >0

Test statistic t=b/SEb=11.263/1.591=7.08

Degree of frredom=n-2=6-2=4

p-value=0.0011 using excel function =TDIST(7.08,4,1)

As p-value<0.05, we reject the null hypothesis and conclude that Distance has a significant positive linear impact on Days

Part-b

Null hypothesis H0:=0 is to be tested against the alternative Ha: 0

Test statistic t=b/SEb=11.263/1.591=7.08

Degree of frredom=n-2=6-2=4

p-value=0.0021 using excel function =TDIST(7.08,4,2)

As p-value<0.05, we reject the null hypothesis and conclude that Distance has a significant linear linear impact on Days

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