Based on observed males using public restrooms, 85% of adult...

Based on observed males using public restrooms, $85\%$ of adult males wash their hands in a public restroom (based on data from the American Society for Microbiology and the American Cleaning Institute). In a survey of 523 adult males, 518 reported that they wash their hands in a public restroom. Assuming that the $85\%$ observed rate is correct, find the probability that among 523 randomly selected adult males, 518 or more wash their hands in a public restroom. What do you conclude?

Based on observed males using public restrooms, $85\%$ of adult males wash their hands in a public restroom (based on data from
the American Society for Microbiology and the American Cleaning Institute). In a survey of 523 adult males, 518 reported that they wash their hands in
a public restroom. Assuming that the $85\%$ observed rate is correct, find the probability that among 523 randomly selected adult males, 518 or more
wash their hands in a public restroom. What do you conclude?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

p-value

The p-value is the probability of obtaining a result equal to or more extreme than the observed result, assuming the null hypothesis is true. A very small p-value suggests that the observed outcome is unlikely under the null hypothesis, indicating the possible need to reject it.

Hypothesis Testing

Hypothesis testing is a framework for deciding whether observed data are consistent with a stated assumption (the null hypothesis). It involves comparing the observed statistic to what would be expected under the null hypothesis and determining if any observed difference is statistically significant.

Normal Approximation

When the number of trials is large and the probability of success is neither very small nor very close to one, the binomial distribution can be approximated using a normal distribution. This simplifies the computation of probabilities by utilizing z-scores and the properties of the normal curve.

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent, identically distributed trials, where each trial has a constant probability of success. This concept is crucial when determining the probability of a particular number of occurrences given the total number of events.

Transcript

Please give Ace some feedback