A simple random sample of 21 people with early onset dementia gave the following

Question

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 conlclude that the mean age at diagnosis of all people with early onset dementia is less than 55 years old? assume the population standard deviation is 6.8 years ( Note x-bar=52.5 years)

obtain the rejection region in terms of x-bar.

Explanation / Answer

null hypothesis: mean =55

alternative hypothesis: mean <55

average of above data X=52.524

for std erro =std deviation/(n)1/2 =1.4839

rejecction region at 0.01 level: z<-2.326

hence test stat z=(X-mean)/std error =(52.524-55)/1.4839=-1.669

as test stat is not in rejection region we can not reject null hypothesis.

data does not provide sufficient evidence to conlclude that the mean age at diagnosis of all people with early onset dementia is less than 55 years old

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