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A simple random sample (SRS) is a fundamental concept in statistics used to ensure that results are unbiased and reliable. It involves selecting a group of participants from a larger population, where each member of the population has an equal chance of being chosen. This ensures that the sample represents the broader population well.

In Glenn's scenario, he selects 50 students randomly from a total of 2400 students at his college. Each student had an equal opportunity to be part of the sample, fulfilling the requirement for a simple random sample. This method is crucial because it helps to avoid any unintentional biases in the data collection process. By using an SRS, Glenn can confidently state that his findings on the proportion of students who think tuition is too high are generalized to the entire student body.

Normal approximation is used when dealing with proportions if certain criteria are met, allowing the sampling distribution of the sample proportion to be shaped like a normal distribution. This approximation simplifies calculations while estimating parameters, such as confidence intervals.

The logic here is that if the sample size is large enough, the distribution of the sample proportion will resemble the normal distribution due to the Central Limit Theorem. In the problem at hand, since Glenn has a sample of 50, we need to ensure that both the expected number of successes (\(np\)) and failures (\(n(1-p)\)) are at least 10 to rely on the normal approximation.

• Successes: \(np = 50 imes 0.76 = 38\).
• Failures: \(n(1-p) = 50 imes 0.24 = 12\).

Both conditions are satisfied, confirming that normal approximation is appropriate for this exercise.

The sample size condition ensures that the normal approximation to the binomial distribution can be applied. This condition requires that both the number of successes and the number of failures in our sample be 10 or more.

In Glenn’s situation, with 38 students out of 50 stating tuition is too high:

• The number of successes is \(np = 38\).
• The number of failures is \(n(1-p) = 12\).

Both these numbers exceed 10, meaning the normal approximation condition based on the sample size is met. Thus, it confirms that we can use the methods associated with the normal distribution to analyze this sample.

The population size condition is another critical requirement for statistical analysis that ensures the independence of sample observations. The rule of thumb is that the sample size should be less than 10% of the total population size.

In Glenn's case, he surveys 50 students out of a population of 2400. Let's break it down:

• Calculate 10% of the population: \(0.1 imes 2400 = 240\).
• Compare with the sample size: 50 students.

Since 50 is far less than 240, this condition is satisfied. This compliance is essential as it confirms that the sample is small enough not to affect the overall population characteristics and that each observation remains independent.