Question

In: Statistics and Probability

Dependent Sample T-Test Researchers were interested in studying whether seniors who participated in Silver Sneakers had...

Dependent Sample T-Test

Researchers were interested in studying whether seniors who participated in Silver Sneakers had a significant weight loss over a 10 week period. Given the above information, answer the questions below (assume a level of significance of .05).

  1. State the null and alternate hypotheses.
  2. What is the independent variable?
  3. What is the dependent variable?
  4. Complete the table below:

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

preweight Weight before the diet (kg)

72.53

78

8.723

.988

weight10weeks Weight after 10 weeks on the diet

68.681

78

8.9245

1.0105

Beginning Weight in kg

Weight after 10 weeks in kg

Sample Size

Sample Mean

Sample Standard Deviation

Estimated Standard Error

Using the information below, answer the following questions:

  1. What is the mean difference?
  2. What was the t value and degrees of freedom?
  3. What was the p value?
  4. Draw a conclusion based on the hypotheses. Phrase it in terms of the original research questions, not just whether you accept or reject the null.

Paired Samples Test

Paired Differences

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Pair 1

Weight before the diet (kg) - Weight after 10 weeks on the diet

3.8449

2.5515

.2889

3.2696

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

95% Confidence Interval of the Difference

Upper

Pair 1

Weight before the diet (kg) - weight10weeks Weight after 10 weeks on the diet

4.4201

13.309

77

.000

Solutions

Expert Solution

Ho :   µd=   0                  
Ha :   µd >   0      
          
................   
Level of Significance ,    α =    0.05       claim:µd=0          
                          
sample size ,    n =    78                  
                          
mean of sample 1,    x̅1=   72.530                  
                          
mean of sample 2,    x̅2=   68.681                  
                          
mean of difference ,    D̅ =    3.849                  
......................


std dev of difference , Sd =        2.5515                  
                          
std error , SE = Sd / √n =    2.5515   / √   78   =   0.2889      
......................

  
t-statistic = (D̅ - µd)/SE = (   3.849   -   0   ) /    0.2889   =   13.323
.......................


Degree of freedom, DF=   n - 1 =    77                  
...................


p-value =        0.0000 [excel function: =t.dist.rt(t-stat,df) ]               
.......................

decision:    p-value <α , Reject null hypothesis              

       
conclusion: there is sufficient evidence to say that seniors who participated in Silver Sneakers had a significant weight loss over a 10 week period

please revert for doubt


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