In minitab again use stat basic statistics 1

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display of the confidence interval.] In Minitab : Again use Stat > Basic Statistics > 1 Proportion but make sure (under Options ) that the alternative is set to “not equal” (e) Use technology to verify the confidence interval endpoints that you found in (c). (f) Use technology to determine a 99% confidence interval for the probability that a kissing couple leans to the right. Comment on how this interval compares to the 95% interval, examining both midpoints and widths. Also indicate whether your answer to (d) turned out to be correct. (g) Interpret the confidence interval from (f). What are you 99% confident of?
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Chance/Rossman, 2015 ISCAM III Investigation 1.5 51 Study Conclusions The researchers are assuming they have a representative sample from a process and want to determine S , the underlying probability that a randomly selected kissing couple leans to the right. Based on this sample of 124 observations, we estimate S to be close to 80/124 = 0.645. However, we know there is some sampling variability, so we want to find an interval of values that appear to be plausible values of S . We do this by finding the values of S for which the two-sided p-value is greater than 0.05. These are all the values of the parameter such that our sample result is not overly surprising. You should have found this “95% confidence” interval to be approximately 0.554 to 0.729 (results from using Minitab or R or the applet will differ slightly). Thus, based on these sample results, we are “confident” that the actual value of S , the probability a random kissing couple leans right, is between 0.55 and 0.73. A 99% confidence interval for S extends from 0.526 and 0.752 and therefore includes more values than a 95% interval. The higher level of confidence requires more “room for error.” You will learn more about confidence intervals in the next section. Discussion: In this investigation you have learned a second t ype of “statistical inference”: based on the sample statistic, providing an interval of plausible values for the parameter. Confidence intervals provide a nice companion to tests of significance and are also very useful by themselves. Whereas a test of significance allows to you test a specific hypothesized value, if you reject the null hypothesis, the test of significance provides no information as to how different the actual parameter is from the hypothesized value. The confidence interval provides an estimate (with bounds) of the actual value of the parameter. In fact, there is a type of duality between confidence intervals and tests of significance. The confidence interval is the set of values for which we would fail to reject the null hypothesis in favor of the two-sided alternative. In fact, Minitab’s algorithm for the two -sided p-value is obtained by maintaining this correspondence (the small p-values approach may lead to small departures from this duality). So we can interpret the confidence interval as the set of plausible values for the parameter in that they are the values such that our observed sample result would not be surprising.
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