Math / Data & Statistics

QuestionFind the critical value $z_{C}$ necessary to form a confidence interval at the level of confidence shown below. $\begin{array}{r} \mathrm{c}=0.94 \\ \mathrm{z}_{\mathrm{c}}=\square \end{array}$ $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. The confidence level $c = 0.94$ .
2. The critical value $z_{c}$ is based on the standard normal distribution.
3. The critical value $z_{c}$ corresponds to the tails of the distribution that are not covered by the confidence level.

STEP 2

1. Determine the area in each tail of the standard normal distribution.
2. Find the critical value $z_{c}$ using the standard normal distribution table or a calculator.

STEP 3

Calculate the total area in both tails of the distribution. Since the confidence level $c = 0.94$ , the area not covered by the confidence interval is:
$1 - c = 1 - 0.94 = 0.06$

STEP 4

Divide the area equally between the two tails:
$\frac{0.06}{2} = 0.03$
Each tail has an area of $0.03$ .

STEP 5

Find the critical value $z_{c}$ such that the cumulative area to the left is $1 - 0.03 = 0.97$ .
Using a standard normal distribution table or calculator, find $z$ such that:
$P(Z < z) = 0.97$

STEP 6

The critical value $z_{c}$ corresponding to a cumulative probability of $0.97$ is approximately:
$z_{c} \approx 1.88$
(Rounded to two decimal places)
The critical value is:
$\boxed{1.88}$

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QuestionFind the critical value $z_{C}$ necessary to form a confidence interval at the level of confidence shown below. $\begin{array}{r} \mathrm{c}=0.94 \\ \mathrm{z}_{\mathrm{c}}=\square \end{array}$ $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. The confidence level $c = 0.94$ .
2. The critical value $z_{c}$ is based on the standard normal distribution.
3. The critical value $z_{c}$ corresponds to the tails of the distribution that are not covered by the confidence level.

STEP 2

1. Determine the area in each tail of the standard normal distribution.
2. Find the critical value $z_{c}$ using the standard normal distribution table or a calculator.

STEP 3

Calculate the total area in both tails of the distribution. Since the confidence level $c = 0.94$ , the area not covered by the confidence interval is:
$1 - c = 1 - 0.94 = 0.06$

STEP 4

Divide the area equally between the two tails:
$\frac{0.06}{2} = 0.03$
Each tail has an area of $0.03$ .

STEP 5

Find the critical value $z_{c}$ such that the cumulative area to the left is $1 - 0.03 = 0.97$ .
Using a standard normal distribution table or calculator, find $z$ such that:
$P(Z < z) = 0.97$

STEP 6

The critical value $z_{c}$ corresponding to a cumulative probability of $0.97$ is approximately:
$z_{c} \approx 1.88$
(Rounded to two decimal places)
The critical value is:
$\boxed{1.88}$

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QuestionFind the critical value zCz_{C}zC​ necessary to form a confidence interval at the level of confidence shown below. c=0.94zc=□\begin{array}{r} \mathrm{c}=0.94 \\ \mathrm{z}_{\mathrm{c}}=\square \end{array}c=0.94zc​=□​ □\square□ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. The confidence level c=0.94 c = 0.94 c=0.94.2. The critical value zc z_{c} zc​ is based on the standard normal distribution.3. The critical value zc z_{c} zc​ corresponds to the tails of the distribution that are not covered by the confidence level.

STEP 2

1. Determine the area in each tail of the standard normal distribution.2. Find the critical value zc z_{c} zc​ using the standard normal distribution table or a calculator.

STEP 3

Calculate the total area in both tails of the distribution. Since the confidence level c=0.94 c = 0.94 c=0.94, the area not covered by the confidence interval is:1−c=1−0.94=0.06 1 - c = 1 - 0.94 = 0.06 1−c=1−0.94=0.06

STEP 4

Divide the area equally between the two tails:0.062=0.03 \frac{0.06}{2} = 0.03 20.06​=0.03Each tail has an area of 0.03 0.03 0.03.

STEP 5

Find the critical value zc z_{c} zc​ such that the cumulative area to the left is 1−0.03=0.97 1 - 0.03 = 0.97 1−0.03=0.97.Using a standard normal distribution table or calculator, find z z z such that:P(Z<z)=0.97 P(Z < z) = 0.97 P(Z<z)=0.97

STEP 6

The critical value zc z_{c} zc​ corresponding to a cumulative probability of 0.97 0.97 0.97 is approximately:zc≈1.88 z_{c} \approx 1.88 zc​≈1.88(Rounded to two decimal places) The critical value is:1.88 \boxed{1.88} 1.88​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the critical value $z_{C}$ necessary to form a confidence interval at the level of confidence shown below. $\begin{array}{r} \mathrm{c}=0.94 \\ \mathrm{z}_{\mathrm{c}}=\square \end{array}$ $\square$ (Round to two decimal places as needed.)

1. The confidence level $c = 0.94$ .
2. The critical value $z_{c}$ is based on the standard normal distribution.
3. The critical value $z_{c}$ corresponds to the tails of the distribution that are not covered by the confidence level.

1. Determine the area in each tail of the standard normal distribution.
2. Find the critical value $z_{c}$ using the standard normal distribution table or a calculator.

Calculate the total area in both tails of the distribution. Since the confidence level $c = 0.94$ , the area not covered by the confidence interval is:
$1 - c = 1 - 0.94 = 0.06$

Divide the area equally between the two tails:
$\frac{0.06}{2} = 0.03$
Each tail has an area of $0.03$ .

Find the critical value $z_{c}$ such that the cumulative area to the left is $1 - 0.03 = 0.97$ .
Using a standard normal distribution table or calculator, find $z$ such that:
$P(Z < z) = 0.97$

The critical value $z_{c}$ corresponding to a cumulative probability of $0.97$ is approximately:
$z_{c} \approx 1.88$
(Rounded to two decimal places)
The critical value is:
$\boxed{1.88}$