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A 1992 article in the Journal of the American Medical Association ("A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body temperature, and Other Legacies of Carl Reinhold August Wundrlich") reported body temperature, gender, and heart rate for a number of subjects. The temperatures for 25 female subjects follow: 97.897.297.497.697.897.998.098.097.998.198.298.398.3 98.498.498.498.598.698.698.798.898.898.998.999.0 Test the hypothesis versus using Round your answers to three decimal places (e.g. 98.765). (a) Calculate the sample mean and standard deviation. Enter your answer; sample mean Enter your answer; standard deviation
A 1992 article in the Journal of the American Medical Association ("A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body temperature, and Other Legacies of Carl Reinhold August Wundrlich") reported body temperature, gender, and heart rate for a number of subjects. The temperatures for 25 female subjects follow: 97.897.297.497.697.897.998.098.097.998.198.298.398.3 98.498.498.498.598.698.698.798.898.898.998.999.0 Test the hypothesis versus using Round your answers to three decimal places (e.g. 98.765). (a) Calculate the sample mean and standard deviation. Enter your answer; sample mean Enter your answer; standard deviation
Answer:a)b)If we compare the p value and the significance level assumedwe see thatso we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is significant different from 98.6 at 5% of significance.Step-by-step explanation:Previous concepts and data givenThemargin of erroris the range of values below and above the sample statistic in a confidence interval.Normal distribution,is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".(a) Calculate the sample mean and standard deviation.The data given is:97.8, 97.2, 97.4, 97.6, 97.8, 97.9, 98.0, 98.0, 97.9, 98.1, 98.2, 98.3, 98.3, 98.4, 98.4, 98.4, 98.5, 98.6, 98.6, 98.7, 98.8, 98.8, 98.9, 98.9, 99.0In order to calculate the sample mean and the sample deviation we can use the following formulas:represent the sample meanrepresent the sample standard deviationn=25 represent the sample selectedsignificance levelb) Test the hypothesis Upper H0:mu= 98.6 versus H1 mu not-equals 98.6State the null and alternative hypotheses.We need to conduct a hypothesis in order to check if the mean is 98.6, the system of hypothesis would be:Null hypothesis:Alternative hypothesis:If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:(1)t-test:"Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".Calculate the statisticWe can replace in formula (1) the info given like this:P-valueFirst we need to calculate the degrees of freedom given by:Since is a two sided test the p value would be:ConclusionIf we compare the p value and the significance level assumedwe see thatso we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is significant different from 98.6 at 5% of significance....