Question

A company manufactures ceramic jugs but customers complain that some of them are cracked. The company wants to investigate if more than 3.43% of the jugs are cracked. To do hypothesis testing, a random sample of 437 jugs is collected from th manufacturing plant and tested. The sample has 4.73% cracked and the company uses a 5% significance level. Find the test-statistic (z-score) associated with the sample proportion in this test. Note: 1- Only round your final answer.

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Answer 1

The test-statistic (z-score) associated with the sample proportion in this test is approximately 2.13.

Step-by-step explanation:

Step 1: Calculate the test statistic (z-score) using the formula:

z = (p - P) / sqrt(P(1-P)/n)

Where:

• p = sample proportion = 0.0473
• P = hypothesized proportion = 0.0343
• n = sample size = 437

Step 2: Substitute the given values into the formula:

z = (0.0473 - 0.0343) / sqrt(0.0343(1-0.0343)/437)

Step 3: Calculate the z-score:

z ≈ 2.13

Step 4: Round the answer:

The test-statistic (z-score) associated with the sample proportion in this test is approximately 2.13.