Answer:
[tex]t = 7.359[/tex]
Step-by-step explanation:
Given
[tex]Range = 60[/tex]
[tex]Min = 5[/tex]
[tex]Max = 65[/tex]
[tex]\bar x = 42.31[/tex]
[tex]\sigma^2 =100.00[/tex]
[tex]\sigma = 10.00[/tex]
[tex]\sum = 1227[/tex]
[tex]n=40[/tex]
Required
The t statistic
This is calculated using:
[tex]t = \frac{\bar x - \mu}{\sigma/\sqrt n}[/tex]
Where
[tex]\mu \to[/tex] Population mean
[tex]\mu = \frac{\sum }{n}[/tex]
[tex]\sum = 1227[/tex] and [tex]n=40[/tex]
[tex]\mu = \frac{1227}{40}[/tex]
[tex]\mu = 30.675[/tex]
So, we have:
[tex]t = \frac{\bar x - \mu}{\sigma/\sqrt n}[/tex]
[tex]t = \frac{42.31 - 30.675}{10/\sqrt{40}}[/tex]
[tex]t = \frac{42.31 - 30.675}{10/6.325}[/tex]
[tex]t = \frac{11.635}{1.581}[/tex]
[tex]t = 7.359[/tex]
