Questions: Find each of the following. Enter your answers rounded to at least two decimal places. Part 1 of 5 zα / 2 for the 95% confidence interval zα / 2=1.96 Part 2 of 5 zα / 2 for the 86% confidence interval zα / 2=1.48 Part 3 of 5 zα / 2 for the 90% confidence interval zα / 2=1.64 Part 4 of 5 zα / 2 for the 99% confidence interval Part 5 of 5 zα / 2 for the 85% confidence interval

Find each of the following. Enter your answers rounded to at least two decimal places.

Part 1 of 5
zα / 2 for the 95% confidence interval
zα / 2=1.96

Part 2 of 5
zα / 2 for the 86% confidence interval
zα / 2=1.48

Part 3 of 5
zα / 2 for the 90% confidence interval
zα / 2=1.64

Part 4 of 5
zα / 2 for the 99% confidence interval

Part 5 of 5
zα / 2 for the 85% confidence interval

Transcript text: Find each of the following. Enter your answers rounded to at least two decimal places. Part 1 of 5 $z_{\alpha / 2}$ for the $95 \%$ confidence interval \[ z_{\alpha / 2}=1.96 \] Part 2 of 5 $z_{\alpha / 2}$ for the $86 \%$ confidence interval \[ z_{\alpha / 2}=1.48 \] Part 3 of 5 $z_{\alpha / 2}$ for the $90 \%$ confidence interval \[ z_{\alpha / 2}=1.64 \] Part 4 of 5 $z_{\alpha / 2}$ for the $99 \%$ confidence interval Part 5 of 5 $z_{\alpha / 2}$ for the $85 \%$ confidence interval

Solution

Solution Steps

Step 1: Convert the given confidence level to a decimal if it is provided as a percentage.

If the confidence level is given as a percentage, it is converted to a decimal. For example, a confidence level of 95% is converted to 0.95.

Step 2: Calculate alpha, which is equal to 1 - confidence level.

Alpha ($lpha$) is calculated as 1 - confidence level, which equals 0.05.

Step 3: Divide alpha by 2 to find alpha / 2.

$lpha / 2$ is calculated as 0.05 / 2, which equals 0.025.

Step 4: Use a standard normal distribution table or statistical software to find the z-score.

The z-score that corresponds to the area of $1 - lpha / 2$ to the left of $z$ is found using statistical software, which gives us a z-score of 1.96.

Final Answer:

The critical value $z_{lpha / 2}$ that corresponds to the given confidence level is 1.96.

Step 1: Convert the given confidence level to a decimal if it is provided as a percentage.

If the confidence level is given as a percentage, it is converted to a decimal. For example, a confidence level of 86% is converted to 0.86.

Step 2: Calculate alpha, which is equal to 1 - confidence level.

Alpha ($lpha$) is calculated as 1 - confidence level, which equals 0.14.

Step 3: Divide alpha by 2 to find alpha / 2.

$lpha / 2$ is calculated as 0.14 / 2, which equals 0.07.

Step 4: Use a standard normal distribution table or statistical software to find the z-score.

The z-score that corresponds to the area of $1 - lpha / 2$ to the left of $z$ is found using statistical software, which gives us a z-score of 1.48.

Final Answer:

The critical value $z_{lpha / 2}$ that corresponds to the given confidence level is 1.48.

Step 1: Convert the given confidence level to a decimal if it is provided as a percentage.

If the confidence level is given as a percentage, it is converted to a decimal. For example, a confidence level of 90% is converted to 0.9.

Step 2: Calculate alpha, which is equal to 1 - confidence level.

Alpha ($lpha$) is calculated as 1 - confidence level, which equals 0.1.

Step 3: Divide alpha by 2 to find alpha / 2.

$lpha / 2$ is calculated as 0.1 / 2, which equals 0.05.

Step 4: Use a standard normal distribution table or statistical software to find the z-score.

The z-score that corresponds to the area of $1 - lpha / 2$ to the left of $z$ is found using statistical software, which gives us a z-score of 1.64.

Final Answer:

The critical value $z_{lpha / 2}$ that corresponds to the given confidence level is 1.64.

Step 1: Convert the given confidence level to a decimal if it is provided as a percentage.

If the confidence level is given as a percentage, it is converted to a decimal. For example, a confidence level of 99% is converted to 0.99.

Step 2: Calculate alpha, which is equal to 1 - confidence level.

Alpha ($lpha$) is calculated as 1 - confidence level, which equals 0.01.

Step 3: Divide alpha by 2 to find alpha / 2.

$lpha / 2$ is calculated as 0.01 / 2, which equals 0.005.

Step 4: Use a standard normal distribution table or statistical software to find the z-score.

The z-score that corresponds to the area of $1 - lpha / 2$ to the left of $z$ is found using statistical software, which gives us a z-score of 2.58.

Final Answer:

The critical value $z_{lpha / 2}$ that corresponds to the given confidence level is 2.58.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!