Respuesta :
Answer:
Mean, x: 7
standard deviation(s)=0.4944
t=-3.1980
Step-by-step explanation:
given data
7.4 7.0 6.5 7.4 7.6 6.2 6.9 7.6 6.5 6.9
Count, N: 10
Sum, Σx: 70
Mean, x: 7
Variance, s2: 0.24444444444444
Steps
s2 = [tex]\frac{∑(xi - x)2}{N - 1}[/tex]
=[tex]\frac{(7.4 - 7)2 + ... + (6.9 - 7)2}{10-1}[/tex]
=[tex]\frac{2.2}{9}[/tex]
=0.24444444444444
s = [tex]\sqrt{0.24444444444444}[/tex]
⇒s= 0.49441323247304
⇒s=0.4944
b) H0: μ = 7.5 versus Ha: μ < 7.5.
α = 0.01.
t=[tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
t=[tex]\frac{7-7.5}{\frac{0.4944}{\sqrt{10} } }[/tex]
t=-3.1980
for 9 df and α = 0.01
t stat from table is -2.82
as t test is less than t
we reject the null hypothesis
