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Mr. Roby is trying to estimate the difference in the proportion of his male students who on average sleep fewer than 6 hours per night compared with his female students. He selects a random sample of 20 of his 75 male students and finds that 5 of them sleep fewer than 6 hours per night. He selects another random sample of 17 of his 100 female students and finds that 8 of them sleep fewer than 6 hours a night.

Check the conditions for constructing a confidence interval for the difference in proportions.

1. Random condition:
- Met

2. 10% condition:

3. Large Counts condition:

Are all the conditions for inference met?

Answer :

Random condition:

Met

10% condition:

Not met

Large Counts condition:

Not met

Are all the conditions for inference met?

No

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Rewritten by : Barada

The large counts condition is met for both samples.

What is random condition ?

The random condition is one of the assumptions necessary for making statistical inferences about a population based on a sample. It requires that the sample be selected randomly from the population, meaning that every individual in the population has an equal chance of being selected for the sample.

The conditions for constructing a confidence interval for the difference in proportions are:

Random condition: The samples must be randomly selected from their respective populations. In this case, Mr. Roby selects random samples of 20 out of 75 male students and 17 out of 100 female students, so this condition is met.

10% condition: The sample sizes should not exceed 10% of their respective populations. Since 20 is less than 10% of 75, and 17 is less than 10% of 100, this condition is met.

Large counts condition: Both sample sizes should be large enough that the expected number of successes and failures in each sample is at least 10. This condition can be checked using the following formulas:

np1 >= 10

np2 >= 10

n(1-p1) >= 10

n(1-p2) >= 10

where np1 and np2 are the expected number of successes in the two samples, n is the total sample size, and p1 and p2 are the proportions of successes in the two populations.

For the male sample, np1 = 20*(5÷20) = 5 and n(1-p1) = 20*(1-5÷20) = 15, both of which are greater than 10. For the female sample, np2 = 17*(8÷17) = 8 and n(1-p2) = 17*(1-8÷17) = 9, both of which are also greater than 10. Therefore, the large counts condition is met for both samples.

So, all the conditions for inference are met in this case, and we can proceed to construct a confidence interval for the difference in proportions.

To learn more about Random condition from given link.

https://brainly.com/question/30482484

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