Respuesta :
Answer:
Step-by-step explanation:
We would use the t- distribution.
From the information given,
Mean, μ = 212.7 pounds
Standard deviation, σ = 15.6 pounds
number of sample, n = 28
Degree of freedom, (df) = 28 - 1 = 27
Alpha level,α = (1 - confidence level)/2
α = (1 - 0.99)/2 = 0.005
We will look at the t distribution table for values corresponding to (df) = 27 and α = 0.005
The corresponding z score is 2.77
We will apply the formula
Confidence interval
= mean ± z ×standard deviation/√n
It becomes
212.7 ± 2.77 × 15.6/√28
= 212.7 ± 2.77 × 2.948
= 212.7 ± 8.17
The lower end of the confidence interval is 212.7 - 8.17 = 204.53 pounds
The upper end of the confidence interval is 212.7 + 8.17 = 220.87 pounds
Answer:
Confidence Interval (204.53, 220.87)
Step-by-step explanation:
Confidence interval is range of values that you can a some % confident that the true mean of the population lies.
The formula for constructing a confidence Interval
X ± z б/√n
Where X is the mean , б is the standard deviation , n is the sample and z is the value for a desired confidence level.
First find z
Degrees of freedom = 28 - 1 = 27
Level of significance = 1-0.99= 0.01
Then we look up this value in the t distribution
z = 2.771
Lower limit = 212.7- 2.771*15.6/√28 =204.53
Upper limit = 212.7+ 2.771*15.6/√28 =220.87
Confidence Interval (204.53, 220.87)
This means that we are 90% confident that the mean weight of Major Legue Baseball players is between 204.53 and 220.87
