John, a college statistics student, is planning his graduation party. He expects 30 friends to attend his party, and he wants to know how many pizzas he should order. John doesn’t have time to query all 30 friends who will attend his party, so he calls just 15 of them and asks how many slices of pizza they plan to eat at the party.John calculates an average of 4 slices of pizza apiece for the 15 friends he called. Identify the following elements from the preceding story:
| Population | Sample | Statistic | Parameter | ||
|---|---|---|---|---|---|
| The 15 friends he called | |||||
| The average number of slices friends attending the party plan to eat | |||||
| All 30 friends attending the party | |||||
| The average number of slices the 15 friends he called said they plan to eat |
After further review, John concludes that the average number of slices for the friends attending his party is less than or equal to 4.1 at a significance level of 10%. This means that John’s conclusion is —————- 10% of the time. Since each pizza has 12 slices, he orders 10 pizzas for his party. correct or incorrect
Planning a successful graduation party involves careful consideration of various factors, such as the number of attendees and their food preferences. In this scenario, John, a college statistics student, aims to organize a memorable party for his friends. To determine the optimal number of pizzas to order, John employs statistical methods based on a sample of his friends’ pizza consumption preferences.
Population: The entire group of friends who will attend John’s graduation party, totaling 30 individuals, represents the population. This is the complete set of interest for his analysis.
Sample: John contacts a subset of his friends, specifically 15 of them, to inquire about the number of pizza slices they plan to consume at the party. This smaller group forms the sample he uses to make an estimation about the entire population’s pizza consumption.
Statistic: The average number of pizza slices that the 15 friends he contacted intend to eat is the statistic in this scenario. John calculates this value by summing up the number of slices reported by each friend and dividing by the number of friends in the sample.
Parameter: The average number of pizza slices that all 30 friends attending the party plan to eat collectively represents the parameter. This is the value John aims to estimate using the information from his sample.
John’s calculations reveal that the average number of slices of pizza the 15 friends he contacted plan to eat is approximately 4 slices per person. However, the ultimate goal is to estimate the average number of slices for all 30 friends attending the party. This value, denoted as the parameter, is inferred based on the information collected from the sample.
After a careful review of the data, John reaches a conclusion: the average number of pizza slices for the friends attending his party is less than or equal to 4.1 slices. He makes this assertion at a significance level of 10%, indicating his confidence level in his conclusion.
When stating that his conclusion holds at a significance level of 10%, John essentially means that if he were to randomly sample different groups of friends from the population and calculate their average pizza consumption, his conclusion would be accurate 90% of the time. In other words, there is a 10% chance that his conclusion might be incorrect due to the randomness of sampling.
Since each pizza consists of 12 slices, John orders 10 pizzas for his party. This decision is based on his estimation that the average pizza consumption per person is around 4 slices, a value he calculated from his sample.
In organizing his graduation party, John employs statistical analysis to make informed decisions about the number of pizzas to order. By distinguishing between the population, sample, statistic, and parameter, he navigates the intricacies of estimation. His conclusion, supported by a 10% significance level, underscores the reliability of his inference while acknowledging a margin of error inherent in statistical analysis. This approach not only ensures an adequate food supply for the party but also showcases the practical application of statistics in real-life scenarios.
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