In an analysis investigating the usefulness of pennies, the cents portions of 11

Question

In an analysis investigating the usefulness of pennies, the cents portions of 115 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 29.4 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.05 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts (a) through (e) below.

x2=?

Pvalue=?

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   =   28.866  
Ha:    sigma   =/   28.866  
              
As we can see, this is a    two   tailed test.      

Getting the test statistic, as              
s = sample standard deviation =    29.4          
sigmao = hypothesized standard deviation =    28.866          
n = sample size =    115          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    118.2568476   [ANSWER]

*************************************

As

df = N - 1 =    114          
              
Hence, the two tailed P value is

P = 0.747061711 [ANSWER]

[Th one tailed P value is 0.373530855, in case you use this in class.]

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