Question

A simple random sample of n = 21 people with early-onset dementia have the mean age at diagnosis of ¯x = 52.3 years and the standard deviation of s = 6.5 years.

(a) At 5% significance level perform a hypotheses test to determine whether mean age at diagnosis of all people with early-onset dementia is di↵erent from 55 years.

(b) Interpret your answer from part (a).

Answer 1

Solution :

$\mu$= 55

$\bar x$ =52.3

S =6.5

n = 21

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :  $\mu$  = 55

Ha : $\mu$    $\neq$ 55

Test statistic = t

= ($\bar x$ - $\mu$ ) / S / $\sqrt$ n

= (52.3 -55) / 6.5 / $\sqrt$ 21

= −1.904

Test statistic = t = −1.904

P-value =0.0715

a ) $\alpha$ = 0.05  

P-value ≥ $\alpha$

0.0715 ≥ 0.05

b ) Do not reject the null hypothesis .

There is insufficient evidence to suggest that