S-IC: Making Inferences and Justifying Conclusions

Making Inferences and Justifying Conclusions

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Making Inferences and Justifying Conclusions treats statistics as a formal process of reasoning from samples to populations. Simulation, randomization, and understanding sampling variability underpin the logic of statistical inference. Reports and studies are evaluated for design quality, bias, and the validity of their conclusions.

S-IC.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.S-IC.2Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?S-IC.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.S-IC.4Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.S-IC.5Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.S-IC.6Evaluate reports based on data.
Example Problems
What is the critical value for constructing a 90% confidence interval?
A restaurant states that no more than 10% of its takeout orders are prepared incorrectly. A food blogger thinks the true error rate is higher. They sample recent orders to investigate.

Let
represent the proportion of incorrect takeout orders.

State the
null hypothesis, , for this test.
The parks department will repaint 5 of 50 trail markers. They number the markers and use the random digit table printed below to choose a simple random sample.

Which markers are in the sample?
What is the critical value for constructing a 95% confidence interval?
Priya was testing versus with a sample of 12 observations. Her test statistic was . Assume that the conditions for inference were met.

What is the approximate
P-value for Priya's test?
Round your answer to the nearest thousandth.
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