Question

About 29% of the population in a large region are between the ages of 40 and 65, according to the country's census. However, only 2% of the 2600 employees at a company in the region are between the ages of 40 and 65. Lawyers might argue that if the company hired people regardless of their age, the distribution of ages would be the same as though they had hired people at random from the surrounding population. Check whether the conditions for using the one-proportion z-test are met.

Are all the conditions satisfied? Select all that apply.
• A. No, the Large Sample Size condition is not satisfied or cannot be reasonably assumed.
B. No, the Independence condition is not satisfied or cannot be reasonably assumed.
© C. No, the Large Population condition is not satisfied or cannot be reasonably assumed.
© D. No, the Random Sample condition is not satisfied or cannot be reasonably assumed
O E. Yes, all conditions are satisfied or can be reasonably assumed

Answer 1

The conditions for using the one-proportion z-test are not satisfied in this case due to the small sample size of employees and the lack of randomness in the selection process.

Step-by-step explanation:

The conditions for using the one-proportion z-test are not satisfied in this case. The Large Sample Size condition is not satisfied because the sample size of 2600 employees is not large enough to consider it representative of the population. Additionally, the Independence condition is not satisfied because it cannot be reasonably assumed that the employees were randomly selected from the population. Therefore, the correct options are A. No, the Large Sample Size condition is not satisfied or cannot be reasonably assumed, and B. No, the Independence condition is not satisfied or cannot be reasonably assumed.

Answer 2

The conditions for using the one-proportion z-test are:

Random Sample: The sample must be randomly selected from the population.

Independence: The sample size must be less than 10% of the population.

Large Sample Size: The number of successes and failures must both be at least 10.

In this case, we can’t determine if the sample is random or not based on the information given. So, option D is correct: “No, the Random Sample condition is not satisfied or cannot be reasonably assumed.”

The other conditions seem to be met: the sample size is less than 10% of the population (2600 employees out of a large region), and the number of successes and failures are both greater than 10 (2% of 2600 employees is 52, which is greater than 10). So options A, B, and C are incorrect.

Option E is also incorrect because not all conditions are satisfied or can be reasonably assumed.

So the correct answer is D: “No, the Random Sample condition is not satisfied or cannot be reasonably assumed.”

Received message. The conditions for using the one-proportion z-test are: 1. Random Sample: The sample must be randomly selected from the population. 2. Independence: The sample size must be less than 10% of the population. 3. Large Sample Size: The number of successes and failures must both be at least 10. In this case, we can't determine if the sample is random or not based on the information given. So, option D is correct: "No, the Random Sample condition is not satisfied or cannot be reasonably assumed." The other conditions seem to be met: the sample size is less than 10% of the population (2600 employees out of a large region), and the number of successes and failures are both greater than 10 (2% of 2600 employees is 52, which is greater than 10). So options A, B, and C are incorrect. Option E is also incorrect because not all conditions are satisfied or can be reasonably assumed. So the correct answer is D: "No, the Random Sample condition is not satisfied or cannot be reasonably assumed."