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At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean.Which of the following conditions for inference have not been met?1. The data are collected using a random sampling method.2. The sample size is large enough to assume normality of the distribution of sample means.3. The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III

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Answer:

Step-by-step explanation:

The sample size is just 20. This is small. The sample size should be at least 30

Also, a good maximum sample size should be less 10% of the population. By checking,

10/100 × 500 = 50

This condition is met

Therefore, the conditions for inference that have not been met is

The sample size is large enough to assume normality of the distribution of sample means.

The correct option is

A. II only

Population distribution is probability distribution that measures the frequency of sample provided. For the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.

Given-

Total students 500.

Total students surveyed by the counselor is 20.

Population distribution

Population distribution is probability distribution that measures the frequency of sample provided.

  • I)The data are collected using a random sampling method- All the students surveyed by the counselor is 20 is collected using a random sampling method. Hence the condition I is met for the inference.

  • II) The sample size is large enough to assume normality of the distribution of sample means- The sample size for the given problem is 20. For a large population the sample size must equal to or greater than the 30.Hence the condition II is not met for the inference.

  • III)The sample size is less than 10 percent of the population size- We have total student 500.  The 10 percent of the population size is,

[tex]P=\dfrac{10\times500}{100}[/tex]

[tex]P=50[/tex]

Here the 10 percent of the population size is 50. Our sample size is 20. Thus the sample size is less than 10 percent of the population size.Hence the condition III is met for the inference.

Hence, for the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.

For more about the population distribution follow the link below-

https://brainly.com/question/6774674

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