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melomori
3 months ago
5

Dewey, Lie, and Howe is a regional branch office of the tax preparation conglomerate Hookem, Billem, Cheatem, and Soakem. One we

ek before the deadline for filing federal income tax returns, the systolic blood pressure of a random sample of 45 employees at Dewey, Lie, and Howe is measured. Based on the observations in this sample, a 95% confidence interval for the mean systolic blood pressure μ of all employees is calculated to be (142, 165). Which of the following statements give a statistically correct, acceptable interpretation of this interval?
a. 95% of the sample of employees have a systolic blood pressure between 122 and 138.
b. We are 95% confident that the interval (122, 138) contains the population mean systolic blood pressure of all employees.
c. If the sampling procedure were repeated many times and the sample mean systolic blood pressure from the observations in each sample were calculated, then 95% of the sample means would be between 122 and 138.
d. The probability that the population mean systolic blood pressure is between 122 and 138 is .95.
e. 95% of the population of employees have a systolic blood pressure between 122 and 138.
f. If the sampling procedure were repeated many times and a 95% confidence interval calculated from the observations in each sample, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure ; (122, 138) is one such interval.
g. We are 95% confident that the population mean systolic blood pressure of all employees is in the interval (122, 138).
h. We are 95% confident that the systolic blood pressures in this sample have a sample mean that is between 122 and 138. On 95% of the days the population mean systolic blood pressure is between 122 and 138.
Mathematics
1 answer:
lawyer [12.5K]3 months ago
6 0

Answer:

b. We are 95% confident that the interval (122, 138) contains the population mean systolic blood pressure of all employees.

g. We are 95% confident that the population mean systolic blood pressure of all employees is in the interval (122, 138).

Step-by-step explanation:

The confidence interval from the question does not align with the confidence interval from the answer choices.

A confidence interval represents a set of values within which we estimate, with a specified level of confidence, that a certain population parameter lies.

In this case, with a range of (122, 138), we are 95% sure that the true population mean systolic blood pressure fits between those two numbers.

This interval is calculated based on data from a sample, but it reflects something regarding the parameter of the population.

It does not indicate probabilities for specific values or sample statistics.

Thus, based on this understanding, the valid statements are:

b. We are 95% confident that the interval (122, 138) contains the population mean systolic blood pressure of all employees.

g. We are 95% confident that the population mean systolic blood pressure of all employees is in the interval (122, 138).

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Step-by-step explanation:

Review the provided matrix

A=\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right]

Let matrix B be defined as

B=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right]

It is stated that

A=B

\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right]=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right]

By comparing the corresponding elements from both matrices, we derive

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b_{31}=3,b_{32}=22,b_{33}=8

Consequently, the needed values are b_{11}=9,b_{12}=-2,b_{13}=3,b_{21}=2,b_{22}=17,b_{23}=0,b_{31}=3,b_{32}=22,b_{33}=8.

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