Question

1. Dementia is the loss of 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.

1. Set up the hypothesis to decide whether the mean age at diagnosis of all people with early-onset dementia is less than 55 years old.

2. Explain what each of the following would mean

   1. Type I error

   2. Type II error

   3. Correct decision

3. Now suppose that the results of carrying out the hypothesis test lead researchers to not reject the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean age at diagnosis of all people with early-onset dementia

   1. is 55 years old.

   2. is less than 55 years old.

4. A simple random sample of 21 people with early-onset dementia gave the following data on age at diagnosis, in years showed a sample mean of x ̄ = 52.5 years. The population standard deviation is σ =6.8 years. 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?

Answer 1