A random sample of n = 12 individuals is selected from a population with µ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297. Use the Distributions tool to help answer the questions that follow.   t Distribution Degrees of Freedom = 21         -3.0-2.0-1.00.01.02.03.0x.5000.50000.000   How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)     If there is no treatment effect, how much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)     Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05. (Show three decimal places.) t-critical = ±    t =     The results indicate: Rejection of the null hypothesis; there is not a significant treatment effect.   Failure to reject the null hypothesis; there is a significant treatment effect.   Failure to reject the null hypothesis; there is not a significant treatment effect.   Rejection of the null hypothesis; there is a significant treatment effect.

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A random sample of n = 12 individuals is selected from a population with µ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297. Use the Distributions tool to help answer the questions that follow.
 

t Distribution

Degrees of Freedom = 21

   
   
-3.0-2.0-1.00.01.02.03.0x.5000.50000.000
 
How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)
 
 
If there is no treatment effect, how much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)
 
 
Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05. (Show three decimal places.)
t-critical = ± 
 
t =
 
 
The results indicate:
Rejection of the null hypothesis; there is not a significant treatment effect.
 
Failure to reject the null hypothesis; there is a significant treatment effect.
 
Failure to reject the null hypothesis; there is not a significant treatment effect.
 
Rejection of the null hypothesis; there is a significant treatment effect.
Expert Solution
Step 1

Provided information is;

sample size(n) = 12

level of significance(α)=0.05

mean for the original population (μ)=70

mean for the treated sample(M) = 74.5 

SS = 297

we know that ;

sample standard deviation(s)=s2 = SSn-1)= 29711

                                                         = 5.1961

                                            

 

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