Question

Dementia is the loss of the intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer’s disease is the most common type of dementia. In the article “Living with Early Onset Dementia: Exploring the Experience and Developing Evidence-Based Guidelines for Practice” (Alzheimer’s Care Quarterly, Vol. 5, Issue 2, pp. 111–122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A simple random sample of 21 people with early-onset dementia gave the following data on age at diagnosis, in years. (60 58 52 58 59 58 51 61 54 59 55 53 44 46 47 42 56 57 49 41 43) At the 1% significance level, do the data provide sufficient evidence to conclude that the mean age at diagnosis of all people with early-onset dementia is less than 55 years old? Assume that the population standard deviation is 6.8 years and note that ¯x = 52.5 years.

Answer 1

Ho :   µ =   55                  
Ha :   µ <   55       (Left tail test)          
                          
Level of Significance ,    α =    0.010                  
population std dev ,    σ =    6.8000                  
Sample Size ,   n =    21                  
Sample Mean,    x̅ = ΣX/n =    52.5000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   6.8000   / √    21   =   1.4839      
Z-test statistic= (x̅ - µ )/SE = (   52.500   -   55   ) /    1.4839   =   -1.685
                          
critical z value, z* =       -2.326   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
p-Value   =   0.0460   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value>α, Do not reject null hypothesis                       
Conclusion: There is not enough evidence to conclude that mean age at diagnosis of all people with early-onset dementia is less than 55 years old