Question

In: Statistics and Probability

4. Let X equal the weight (in grams) of a Hershey’s grape-flavored Jolly Rancher. Denote the...

4. Let X equal the weight (in grams) of a Hershey’s grape-flavored Jolly Rancher. Denote the median of X by m. We wish to test the null hypothesis H0 : m = 5.900 against the alternative Ha : m > 5.900. A random sample of size n = 25 yielded the following ordered data:

5.625 5.665 5.697 5.837 5.863 5.870 5.878 5.884 5.908 5.967 6.019 6.020 6.029 6.032 6.037 6.045 6.049 6.050 6.079 6.116 6.159 6.186 6.199 6.307 6.387

Explain step by step how to use a t test to test the hypothesis.

Solutions

Expert Solution

Ho :   µ =   5.9
Ha :   µ >   5.9

sample std dev ,    s =    0.184680517  
Sample Size ,   n =    25  
Sample Mean,    x̅ =   6.00

  
          
degree of freedom=   DF=n-1=   24  
          
Standard Error , SE =   s/√n =   0.0369  
          
t-test statistic=   (x̅ - µ )/SE =    2.608

  

α=0.05


          
critical t value, t*   =   1.7109   [Excel formula =t.inv(α,df) ]

(also, p-value=0.0077)
          
Conclusion: t-stat >t-criitcal value, Reject null hypothesis



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