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Answer :
At a significance level of 0.01, the test statistic (z) is approximately 2.36, which does not exceed the critical value of ±2.58. Therefore, we do not reject the null hypothesis. There is no significant difference between the two suppliers in terms of the proportion of defectives.
To determine if there is a significant difference between the two suppliers of solar panels in terms of the proportion of defectives, we can perform a hypothesis test using the two-sample proportion test.
Let's set up the hypotheses:
Null Hypothesis (H0): The proportion of defectives is the same for both suppliers.
Alternative Hypothesis (Ha): The proportion of defectives is different for the two suppliers.
Step 1: Calculate the sample proportions:
For Supplier A: [tex]\hat{p}[/tex]₁ = 30/600 = 0.05
For Supplier B: [tex]\hat{p}[/tex]₂ = 10/400 = 0.025
Step 2: Calculate the pooled sample proportion:
[tex]\hat{p}[/tex] = (x₁ + x₂) / (n₁ + n₂)
where x₁ and x₂ are the number of defectives for each supplier, and n₁ and n₂ are the sample sizes.
In this case, [tex]\hat{p}[/tex] = (30 + 10) / (600 + 400) = 0.04
Step 3: Calculate the standard error:
SE = √(([tex]\hat{p}[/tex] * (1 - [tex]\hat{p}[/tex]) * ((1 / n₁) + (1 / n₂))))
In this case, SE = √((0.04 * (1 - 0.04) * ((1 / 600) + (1 / 400)))) ≈ 0.0106
Step 4: Calculate the test statistic:
z = ([tex]\hat{p}[/tex]₁ - [tex]\hat{p}[/tex]₂) / SE
In this case, z = (0.05 - 0.025) / 0.0106 ≈ 2.36
Step 5: Determine the critical value:
At a significance level of 0.01 and a two-tailed test, the critical value is approximately z = ±2.58.
Step 6: Compare the test statistic to the critical value:
Since 2.36 is within the range of -2.58 to 2.58, we do not reject the null hypothesis.
Step 7: Make a conclusion:
Based on the results, there is not enough evidence to suggest a significant difference between the two suppliers in terms of the proportion of defectives at a significance level of 0.01.
To know more about null hypothesis;
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