Question

A company manufactures ceramic jugs but customers complain that some of them are cracked. The company wants to investigate if more than 1.79% of the jugs are cracked. To do hypothesis testing, a random sample of 474 jugs is collected from the manufacturing plant and tested. The sample has 4.81% 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. 2- Round your final answer to

3
​
decimal places. Enter your final answer with 3 decimal places. 3- Your final answer (proportion) should not be stated a percentage.

Answer 1

The z-score is calculated using the formula for a test statistic in a proportion hypothesis test by subtracting the null hypothesis proportion from the sample proportion, and then dividing by the standard error. For this case, the test statistic (z-score) is approximately 4.957.

Step-by-step explanation:

To calculate the test statistic (z-score) associated with the sample proportion, we can use the formula for a test statistic in a proportion hypothesis test:

z = (p' - P0)/sqrt(P0(1-P0)/n)

where p' is the sample proportion, P0 is the null hypothesis proportion, and n is the sample size. For this case:

z = (0.0481 - 0.0179)/sqrt(0.0179 * (1 - 0.0179) / 474)

z = 0.0302 / sqrt(0.0179 * 0.9821 / 474)

z = 0.0302 / sqrt(0.01758679 / 474)

z = 0.0302 / sqrt(0.00003710626174)

z = 0.0302 / 0.0060930462203

A calculated z ratio of approximately 4.957 rounded to 4.957, which is our test statistic.