Of 250 college students taking a statistics class, 4...

Name: Problem 79, Chapter 8: Applied Statistics in Business and Economics
Uploaded: 2023-03-11T06:48:18-08:00
Duration: 1 min 41 s
Channel: Dominador Tan
Description: Of 250 college students taking a statistics class, 4 reported an allergy to peanuts. (a) Is the criterion for normality met? (b) Assuming that this was a random sample, use MINITAB to construct a 95 percent confidence interval for the proportion of all college statistics students with a peanut allergy.

Of 250 college students taking a statistics class, 4 reported an allergy to peanuts. (a) Is the criterion for normality met? (b) Assuming that this was a random sample, use MINITAB to construct a 95 percent confidence interval for the proportion of all college statistics students with a peanut allergy.

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Key Concepts

Confidence_Interval_for_a_Proportion

A confidence interval for a proportion is an estimated range of values which is likely to include the true population proportion. It is constructed using the sample proportion, the estimated standard error derived from the assumption of normality, and a critical value corresponding to the desired confidence level (such as 1.96 for a 95 percent confidence level). This interval quantifies the uncertainty in estimating the population proportion from a sample.

Random_Sampling

Random sampling is a fundamental concept in statistics where each member of the population has an equal chance of being selected in the sample. This ensures that the sample is representative of the population, reducing bias and allowing for more generalizable inferences about the population based on the sample data.

Normality_Sampling_Distribution

This concept refers to the condition under which data can be approximated by a normal distribution, typically checked in proportion problems by ensuring that both np and n(1-p) are at least 10. Meeting this criterion allows the use of the normal approximation in constructing confidence intervals or conducting hypothesis tests for proportions.

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