The test statistic of $$ z=-1.18 $$ is obtained when testing the claim that $$ p
eq 0.513 $$. This is a two-tailed test. Using a 0.05 significance level, complete parts (a) and (b). Click here to view the standard normal distribution table for negative $$ z $$ scores. Click here to view the standard normal distribution table for positive $$ z $$ scores. a. Find the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. There are two critical values, the lower critical value is $$ \square $$ and the upper critical value is is one critical value; the critical value is B. There

Question

The test statistic of $$ z=-1.18 $$ is obtained when testing the claim that $$ p 
eq 0.513 $$. This is a two-tailed test. Using a 0.05 significance level, complete parts (a) and (b). Click here to view the standard normal distribution table for negative $$ z $$ scores. Click here to view the standard normal distribution table for positive $$ z $$ scores. a. Find the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. There are two critical values, the lower critical value is $$ \square $$ and the upper critical value is is one critical value; the critical value is B. There

UpStudy AI · Accepted Answer

To find the critical values for a two-tailed test at a significance level of $$ \alpha = 0.05 $$, we need to determine the z-scores that correspond to the tails of the standard normal distribution.

1. Since this is a two-tailed test, we will split the significance level into two tails:
   - Each tail will have an area of $$ \frac{0.05}{2} = 0.025 $$.

2. We will look for the z-scores that correspond to the cumulative probabilities of $$ 0.025 $$ and $$ 0.975 $$ (since $$ 1 - 0.025 = 0.975 $$).

Now, let's find the critical values using the standard normal distribution.

- The critical value for the lower tail (z-score for $$ 0.025 $$).
- The critical value for the upper tail (z-score for $$ 0.975 $$).

Let's calculate these values.

The critical values are typically found in z-tables or using statistical software.

For $$ z $$ corresponding to $$ 0.025 $$ and $$ 0.975 $$:

- $$ z_{0.025} $$ is approximately $$ -1.96 $$.
- $$ z_{0.975} $$ is approximately $$ 1.96 $$.

Thus, the critical values are:

- Lower critical value: $$ -1.96 $$
- Upper critical value: $$ 1.96 $$

Now, I will summarize the results for part (a).

### Part (a) Answer:
A. There are two critical values, the lower critical value is $$ -1.96 $$ and the upper critical value is $$ 1.96 $$.
The critical values are $$ -1.96 $$ and $$ 1.96 $$.

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