A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 5% significance level. x= 33, n= 32, o = 4, Ho: = 35, H: u < 35 The test statistic is z= (Round to two decimal places as needed.) Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. The critical values are t Za/2= + O B. The critical value is za = n O c. The critical value is -z,= the null hypothesis. The data V sufficient evidence to conclude that the mean is
A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 5% significance level. x= 33, n= 32, o = 4, Ho: = 35, H: u < 35 The test statistic is z= (Round to two decimal places as needed.) Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. The critical values are t Za/2= + O B. The critical value is za = n O c. The critical value is -z,= the null hypothesis. The data V sufficient evidence to conclude that the mean is
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![## One-Mean Z-Test: Hypothesis Testing
### Problem Statement
A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 5% significance level.
Given:
- \( \bar{x} = 33 \)
- \( n = 32 \)
- \( \sigma = 4 \)
- \( H_0: \mu = 35 \)
- \( H_a: \mu < 35 \)
### Step-by-Step Solution:
1. **Calculate the Test Statistic (Z):**
The formula for the test statistic \( Z \) in a one-mean z-test is given by:
\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
\( \bar{x} \) is the sample mean, \( \mu \) is the population mean, \( \sigma \) is the population standard deviation, and \( n \) is the sample size.
Calculation:
\[
Z = \frac{33 - 35}{\frac{4}{\sqrt{32}}}
\]
Round to two decimal places as needed.
2. **Identify the Critical Value(s):**
- For a left-tailed test at the 5% significance level, the critical value \( Z_{\alpha} \) can be found using a standard normal distribution table or z-table.
Options include:
- (A) The critical values are \( \pm Z_{\alpha/2} \).
- (B) The critical value is \( Z_{\alpha} \).
- (C) The critical value is \( -Z_{\alpha} \).
For this test:
- Identify and round the critical value to three decimal places as needed.
3. **Make a Decision:**
Compare the test statistic with the critical value:
- If \( Z \) is less than the critical value \( -Z_{\alpha} \), reject the null hypothesis \( H_0 \).
- Select the appropriate option:
- Fail to reject \( H_0 \) if \( Z \) does not fall in the rejection region.
- Reject \( H_0 \) if \( Z \) falls in the rejection region.
Formulate the conclusion based on whether there is sufficient evidence to conclude that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5c84145-a33d-498c-9246-5dc8646df0e1%2Fe23e932c-78f8-4602-a155-e12231ec4388%2Fq7u37g4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## One-Mean Z-Test: Hypothesis Testing
### Problem Statement
A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 5% significance level.
Given:
- \( \bar{x} = 33 \)
- \( n = 32 \)
- \( \sigma = 4 \)
- \( H_0: \mu = 35 \)
- \( H_a: \mu < 35 \)
### Step-by-Step Solution:
1. **Calculate the Test Statistic (Z):**
The formula for the test statistic \( Z \) in a one-mean z-test is given by:
\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
\( \bar{x} \) is the sample mean, \( \mu \) is the population mean, \( \sigma \) is the population standard deviation, and \( n \) is the sample size.
Calculation:
\[
Z = \frac{33 - 35}{\frac{4}{\sqrt{32}}}
\]
Round to two decimal places as needed.
2. **Identify the Critical Value(s):**
- For a left-tailed test at the 5% significance level, the critical value \( Z_{\alpha} \) can be found using a standard normal distribution table or z-table.
Options include:
- (A) The critical values are \( \pm Z_{\alpha/2} \).
- (B) The critical value is \( Z_{\alpha} \).
- (C) The critical value is \( -Z_{\alpha} \).
For this test:
- Identify and round the critical value to three decimal places as needed.
3. **Make a Decision:**
Compare the test statistic with the critical value:
- If \( Z \) is less than the critical value \( -Z_{\alpha} \), reject the null hypothesis \( H_0 \).
- Select the appropriate option:
- Fail to reject \( H_0 \) if \( Z \) does not fall in the rejection region.
- Reject \( H_0 \) if \( Z \) falls in the rejection region.
Formulate the conclusion based on whether there is sufficient evidence to conclude that
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