\( \because \) CENGAGE \( \mid \) MINDTAP Problem Set: Chapter 09 Introduction to the t Statistic to Assignment Properties of a confidence interval suppose the mean of a population is \( \mu=36 \). A researcher (who doe lot know that \( \mu=36 \) ) selects a random sample of size \( n \) from this opulation. Then he constructs a \( 90 \% \) confidence interval of the opulation mean. he true population mean and the researcher's \( 90 \% \) confidence hterval of the population mean are shown in the following graph. Us he graph to answer the questions that follow. ? Jse the grey star to mark the mean of the sample. (Be sure to place he star on the horizontal blue line segment that represents the onfidence interval.) Explanation: The confidence interval is constructed around the sample mean. Thus, the sample mean is located exactly in the center of the confidence interval. In this case, the center of the confidence interval is 40.5. You can see this visually, or simply average the lower and upper ends of the confidence interval: \( M=(38+43) / 2 \) 40.5. o construct the confidence interval, the quantity \( \mathrm{ts}_{\mathrm{m}} \) is subtracted rom and added to the sample mean. \( n \) this case, \( \mathrm{ts}_{\mathrm{M}}=\square \mathrm{x} \).
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Step 1: Read the lower and upper endpoints of the 90% confidence interval from the graph: lower = 38 and upper = 43. Show more…
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