Respuesta :
Solution :
a). Standard error of sample mean = [tex]$\frac{\sigma}{\sqrt n}$[/tex]
[tex]$=\frac{0.5}{\sqrt{15}}$[/tex]
= 0.1290994
The observed mean point be [tex]$\overline x$[/tex]
Test statistics z = [tex]$\frac{\text{(observed mean - hypothesized mean)}}{\text{standard error}}$[/tex]
[tex]$=\frac{\overline x -5}{0.1290994}$[/tex]
For the left one sided test, critical value of z to reject [tex]$H_0 = -1.64$[/tex]
We reject [tex]$H_0$[/tex] when test statics z < -1.64
b). Value of [tex]$\overline x$[/tex] z < -1.64
[tex]$=\frac{(\overline x-5)}{0.1290994}<-1.64$[/tex]
[tex]$=\overline x < 5-0.1290994 \times 1.64$[/tex]
[tex]$=\overline x < 4.78828$[/tex]
∴ we reject [tex]$H_0$[/tex] when [tex]$\overline x < 4.78828$[/tex]
c). The probability of rejecting [tex]$H_0$[/tex] when [tex]$\mu = 4.7$[/tex],
[tex]$P(x<4.788277) = P \left(z < \left(\frac{4.788277-4.7}{0.1290994}\right)\right)$[/tex]
[tex]$=P(z<0.68)$[/tex]
[tex]$=0.7517$[/tex]
