Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Let's solve the problem step by step to arrive at the correct conclusion for the significance test.
### Step 1: Understand the Hypotheses
We are testing the claim that the proportion of defective chips is higher at plant A than at plant B. This can be stated in terms of the following hypotheses:
- Null hypothesis (\(H_0\)): \( p_A - p_B = 0 \) (There is no difference in the proportion of defective chips between plant A and plant B)
- Alternative hypothesis (\(H_1\)): \( p_A - p_B > 0 \) (Plant A has a higher proportion of defective chips than plant B)
### Step 2: Given Data
- Sample size from plant A (\(n_A\)): 80
- Number of defective chips from plant A: 12
- Sample size from plant B (\(n_B\)): 90
- Number of defective chips from plant B: 10
### Step 3: Significance Level
- Significance level (\(\alpha\)): 0.05
### Step 4: P-Value
It is given that the p-value for this test is 0.225.
### Step 5: Compare P-Value with Significance Level
To determine whether we reject or fail to reject the null hypothesis, we need to compare the p-value to the significance level (\(\alpha\)):
- If the p-value \(\leq \alpha\), we reject the null hypothesis.
- If the p-value \(> \alpha\), we fail to reject the null hypothesis.
Given that the p-value (0.225) is greater than the significance level (0.05):
[tex]\[0.225 > 0.05 \][/tex]
### Step 6: Draw Conclusion
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that the proportion of defective computer chips is significantly greater at plant A than at plant B.
Thus, the correct conclusion is:
The owner should fail to reject the null hypothesis since \(0.225 > 0.05\). There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant A.
So the correct option is:
The owner should fail to reject the null hypothesis since [tex]$0.225>0.05$[/tex]. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant [tex]$A$[/tex].
This corresponds to option 4.
### Step 1: Understand the Hypotheses
We are testing the claim that the proportion of defective chips is higher at plant A than at plant B. This can be stated in terms of the following hypotheses:
- Null hypothesis (\(H_0\)): \( p_A - p_B = 0 \) (There is no difference in the proportion of defective chips between plant A and plant B)
- Alternative hypothesis (\(H_1\)): \( p_A - p_B > 0 \) (Plant A has a higher proportion of defective chips than plant B)
### Step 2: Given Data
- Sample size from plant A (\(n_A\)): 80
- Number of defective chips from plant A: 12
- Sample size from plant B (\(n_B\)): 90
- Number of defective chips from plant B: 10
### Step 3: Significance Level
- Significance level (\(\alpha\)): 0.05
### Step 4: P-Value
It is given that the p-value for this test is 0.225.
### Step 5: Compare P-Value with Significance Level
To determine whether we reject or fail to reject the null hypothesis, we need to compare the p-value to the significance level (\(\alpha\)):
- If the p-value \(\leq \alpha\), we reject the null hypothesis.
- If the p-value \(> \alpha\), we fail to reject the null hypothesis.
Given that the p-value (0.225) is greater than the significance level (0.05):
[tex]\[0.225 > 0.05 \][/tex]
### Step 6: Draw Conclusion
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that the proportion of defective computer chips is significantly greater at plant A than at plant B.
Thus, the correct conclusion is:
The owner should fail to reject the null hypothesis since \(0.225 > 0.05\). There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant A.
So the correct option is:
The owner should fail to reject the null hypothesis since [tex]$0.225>0.05$[/tex]. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant [tex]$A$[/tex].
This corresponds to option 4.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
