Please help me with this question ### Hypothesis Testing Using One-Mean Z-Test#### Problem StatementA sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical-value approach.#### Given Data- Sample mean ($ \overline{x} $): 51- Sample size ($ n $): 46- Population standard deviation ($ \sigma $): 3.6- Null hypothesis ($ H_0 $): $ \mu = 50 $- Alternative hypothesis ($ H_a $): $ \mu > 50 $- Significance level ($ \alpha $): 0.01#### Choices1. $ z = 0.28 $; critical value = 2.33; do not reject $ H_0 $2. $ z = 1.884 $; critical value = 2.33; reject $ H_0 $3. $ z = 1.884 $; critical value = 1.33; reject $ H_0 $4. $ z = 1.884 $; critical value = 2.33; do not reject $ H_0 $#### Explanation:1. **Choice A**: - $ z = 0.28 $ - Given the critical value of 2.33. - Since $ 0.28 < 2.33 $, we do not reject $ H_0 $.2. **Choice B**: - $ z = 1.884 $ - Given the critical value of 2.33. - Since $ 1.884 < 2.33 $, we do not reject $ H_0 $.3. **Choice C**: - $ z = 1.884 $ - Given the critical value of 1.33. - Since $ 1.884 > 1.33 $, we reject $ H_0 $.4. **Choice D**: - $ z = 1.884 $ - Given the critical value of 2.33. - Since $ 1.884 < 2.33 $, we do not reject $ H_0 $.#### Conclusion:Based on the given choices, the correct conclusion is provided when $ z $

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Description: Please help me with this question ### Hypothesis Testing Using One-Mean Z-Test#### Problem StatementA sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given

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A sample mean, sample size, and population standard deviation are given. Uso ihe one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical-value approach. x= 51, n= 46 , a= 3.6, Ho: u= 50; H > 50, a = 0.01

A sample mean, sample size, and population standard deviation are given. Uso ihe one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical-value approach. x= 51, n= 46 , a= 3.6, Ho: u= 50; H > 50, a = 0.01

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### Hypothesis Testing Using One-Mean Z-Test

#### Problem Statement
A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical-value approach.

#### Given Data
- Sample mean ($ \overline{x} $): 51
- Sample size ($ n $): 46
- Population standard deviation ($ \sigma $): 3.6
- Null hypothesis ($ H_0 $): $ \mu = 50 $
- Alternative hypothesis ($ H_a $): $ \mu > 50 $
- Significance level ($ \alpha $): 0.01

#### Choices
1. $ z = 0.28 $; critical value = 2.33; do not reject $ H_0 $
2. $ z = 1.884 $; critical value = 2.33; reject $ H_0 $
3. $ z = 1.884 $; critical value = 1.33; reject $ H_0 $
4. $ z = 1.884 $; critical value = 2.33; do not reject $ H_0 $

#### Explanation:
1. **Choice A**:
- $ z = 0.28 $
- Given the critical value of 2.33.
- Since $ 0.28 < 2.33 $, we do not reject $ H_0 $.

2. **Choice B**:
- $ z = 1.884 $
- Given the critical value of 2.33.
- Since $ 1.884 < 2.33 $, we do not reject $ H_0 $.

3. **Choice C**:
- $ z = 1.884 $
- Given the critical value of 1.33.
- Since $ 1.884 > 1.33 $, we reject $ H_0 $.

4. **Choice D**:
- $ z = 1.884 $
- Given the critical value of 2.33.
- Since $ 1.884 < 2.33 $, we do not reject $ H_0 $.

#### Conclusion:
Based on the given choices, the correct conclusion is provided when $ z $

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