Untreated: 37, 42, 31, 29, 49 Treated: 49, 55, 79, 62, 68 3) Test the following

Question

Untreated: 37, 42, 31, 29, 49  

Treated:      49, 55, 79, 62, 68

3) Test the following claims about the mean and standard deviation of the treated group. Use a 0.05 level of significance.

It will take 30 days to display symptoms of the Ebola-Shiva virus.

Step 1: Write hypothesis

H0:   

H1:  

Step 2: Gather data and identify type of test.

Step 3: Find the P-value and test statistic using TI.

               

Step 4: Test hypothesis and state conclusion

The Ebola-Shiva virus will have a standard deviation of less than 7 days to display symptoms.

Step 1: Write hypothesis

H0:

H1:

Step 2: Gather data and identify type of test and critical value(s).

Step 3: Find 2 and P-Value.

Step 4: Test hypothesis and state conclusion

Untreated: 37, 42, 31, 29, 49  

Treated:      49, 55, 79, 62, 68

Explanation / Answer

Part (a)

Step 1

H0: µ = µ0 = 30

H1:  µ 30

Step 2:

Test to be employed is 0ne-sample t-test.

Data: Number of days taken to show symptoms in treated group. Given

49, 55, 79, 62, 68

Step 3:

Test statistic

t = t = (n)(Xbar - µ0)/s, where

Xbar = sample mean, µ0 (given), s = sample standard deviation and n = sample size.

Using Excel Functions on the above data, Xbar = 62.6 and s = 11.633185

So, tcal = (5)(62.6 - 30)/11.63185 = 6.267    

Under H0, t ~ tn – 1

p-value = P(t4 > | 6.267 |) = 0.0066 [using Excel Function]  

        

Step 4:

Given a 0.05 level of significance, since p-value < 0.05, H0 is rejected.

Conclusion

Evidence is not sufficient to validate the claim that Ebola-Shiva takes 30 days to display symptoms in the treated group.

DONE

Part (b)

Step 1

H0: 2 = 20 = 72 = 49

H1:  2 < 49

Step 2:

Test to be employed is chi-square test.

Data: Number of days taken to show symptoms in treated group. Given

49, 55, 79, 62, 68

Step 3:

Test statistic

2 = (n - 1)s2/20

So, 2cal = (4)(11.63185)2/49 = 11.045   

Under H0, 2 ~ 2n – 1

p-value = P(24 < 11.045 = 0.973 [using Excel Function]          

Step 4:

Given a 0.05 level of significance, since p-value > 0.05, H0 is accepted

=>H1 is rejected.

Conclusion

Evidence is not sufficient to validate the claim that standard deviation of the number of days Ebola-Shiva takes to display symptoms in the treated group is less than 7.

DONE

Step 1

H0: µ = µ0 = 30

H1:  µ 30

Step 2:

Test to be employed is 0ne-sample t-test.

Data: Number of days taken to show symptoms in treated group. Given

49, 55, 79, 62, 68

Step 3:

Test statistic

t = t = (n)(Xbar - µ0)/s, where

Xbar = sample mean, µ0 (given), s = sample standard deviation and n = sample size.

Using Excel Functions on the above data, Xbar = 62.6 and s = 11.633185

So, tcal = (5)(62.6 - 30)/11.63185 = 6.267    

Under H0, t ~ tn – 1

p-value = P(t4 > | 6.267 |) = 0.0066 [using Excel Function]  

        

Step 4:

Given a 0.05 level of significance, since p-value < 0.05, H0 is rejected.

Conclusion

Evidence is not sufficient to validate the claim that Ebola-Shiva takes 30 days to display symptoms in the treated group.

DONE

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