Respuesta :
Answer:
a) Sample mean = 9.99
Sample standard deviation = 0.3348
b) -1.0389
c) 0.1631
Step-by-step explanation:
We are given the following in the question:
9.7, 9.9, 10.3, 10.1, 10.5, 9.4, 9.9, 10.1, 9.7, 10.3
a) sample mean and standard deviation
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{99.9}{10} = 9.99[/tex]
Sum of squares of differences = 1.009
[tex]S.D = \sqrt{\dfrac{1.009}{9}} = 0.3348[/tex]
b) observed value of the t-statistic
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{9.99 - 10.1}{\frac{0.3348}{\sqrt{10}} } = -1.0389[/tex]
c) probability of these statistics (or worse) if the true mean were 10.1 mm
Degree of freedom = n - 1 = 9
Calculating the value from the table
[tex]P(x < 9.99) = 0.1631[/tex]
0.1631 is the the probability of these statistics (or worse) if the true mean were 10.1 mm
