Question

1. Volunteers who had developed a cold within the previous 24 hours were randomly assigned to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was 4.5 days with a standard deviation of 1.6 days. For the placebo group, the mean overall duration of symptoms was 8.1 days with a standard deviation of 1.8 days. Assume normal distributions. Test the claim that the mean for the population taking zinc lozenges is less than 8.1 at a .02 level of significance.

1. Identify the proper Test or Confidence interval:

2. Complete the Test or Confidence Interval.

Answer 1

1 sample t test....

Ho :   µ =   8.1                  
Ha :   µ <   8.1       (Left tail test)          
                          
Level of Significance ,    α =    0.02                  
sample std dev ,    s =    1.6000                  
Sample Size ,   n =    25                  
Sample Mean,    x̅ =   4.5000                  
                          
degree of freedom=   DF=n-1=   24                  
                          
Standard Error , SE = s/√n =   1.6000   / √    25   =   0.3200      
t-test statistic= (x̅ - µ )/SE = (   4.500   -   8.1   ) /    0.3200   =   -11.25
                          
p-Value   =   0.0000   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis                       

Level of Significance ,    α =    0.02          
degree of freedom=   DF=n-1=   24          
't value='   tα/2=   2.4922   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   1.6000   / √   25   =   0.320000
margin of error , E=t*SE =   2.4922   *   0.32000   =   0.797491
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    4.50   -   0.797491   =   3.702509
Interval Upper Limit = x̅ + E =    4.50   -   0.797491   =   5.297491
98%   confidence interval is (   3.70   < µ <   5.30   )

                          

THANKS

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