B/C = K/L because they are similar
Answer:
a) For the 90% confidence interval the value of
and
, with that value we can find the quantile required for the interval in the t distribution with df =3. And we can use the folloiwng excel code: "=T.INV(0.05,3)" and we got:
b) For the 99% confidence interval the value of
and
, with that value we can find the quantile required for the interval in the t distribution with df =106. And we can use the folloiwng excel code: "=T.INV(0.005,106)" and we got:
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
Part a
For the 90% confidence interval the value of
and
, with that value we can find the quantile required for the interval in the t distribution with df =3. And we can use the folloiwng excel code: "=T.INV(0.05,3)" and we got:
Part b
For the 99% confidence interval the value of
and
, with that value we can find the quantile required for the interval in the t distribution with df =106. And we can use the folloiwng excel code: "=T.INV(0.005,106)" and we got:
Answer: it Depends
Step-by-step explanation:
Not enough info given
Answer:
x = 65
Step-by-step explanation:
To solve the equation, we write it in radical form:
![5\, \sqrt[3]{x-1} = 20](https://tex.z-dn.net/?f=5%5C%2C%20%5Csqrt%5B3%5D%7Bx-1%7D%20%3D%2020)
Then, we divide both sides by 5 to isolate the root:
![\sqrt[3]{x-1} = \frac{20}{5} \\\sqrt[3]{x-1} =4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx-1%7D%20%3D%20%5Cfrac%7B20%7D%7B5%7D%20%5C%5C%5Csqrt%5B3%5D%7Bx-1%7D%20%3D4)
and next, we raise both sides of the equation to the power 3 so as to free the expression in x from the root:

now we add 1 to both sides to isolate x:
x = 65
It would be D. Very positive!!