The claim that 90% of Americans check their mail daily is tested. Also assume that the initial conclusion rejects the null hypothesis. State the final conclusion in simple, nontechnical terms

Answer: There is sufficent evidence to reject the claim that percentage of Americans who check their mail everyday is equal to 90%

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The statistical method would be to conduct a simple survey, taking a random sample of Americans and asking the simple yes-no question: “Do you check your mail every day?” So the results would just be so many yesses and so many nos, a simple proportion. The stated claim becomes the null hypothesis for the purpose of testing, that is, 90%, or 0.9, of the results of the survey should be yes. The alternative hypothesis is that the figure differs from 90%.

The survey finds that the figure is not 90% and the initial conclusion is to reject the claim. But how confident can we be that our conclusion is representative of all Americans? So a confidence level is set, for example, 95% certainty. From this confidence level we can say that we can expect detailed analysis to show that there is a less than 5% probability that our results are due to chance. After analysis this is what’s found and this gives us confidence that we can reject the claim (the null hypothesis) and establish the counterclaim (the alternative hypothesis) that the figure of 90% is incorrect.

To publish the result of the findings of the analysis, we state that we (are 95% certain that we) have sufficient evidence (the sample data) to reject the claim (null hypothesis) that 90% of Americans check their mail every day.

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