Question 5 > Heights of adults: Researchers studying anthropometry collected body girth measurements and skeletal diamet

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Question 5 > Heights of adults: Researchers studying anthropometry collected body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender, for 507 physically active individuals. The summary statistics below shows the sample distribution of heights in centimeters (Heinz, 2003). Min 147.2 163.8 Q1 Median 170.3 Mean 171.1 SD 9.4 Q3 177.8 Max 198.1 a) What is the point estimate for the average height of active individuals? cm b) What is the median height of these active individuals? cm c) What is the point estimate for the standard deviation of the heights of active individuals? cm d) The interquartile range extends from cm to cm, giving an IQR of cm.

e) is a person who is 1m 80cm (180cm) tall considered unusually tall? And is a person who is 1m 55cm (155cm) considered unusually short? O We cannot tell from the given information O No people can come in all sizes, we cannot define usual or unusual heights O No, they are not unusual since these heights are within two standard deviations of the mean Yes, they are unusual since these heights are more than two standard deviations away from the mean f) The researchers take another random sample of physically active individuals. Would you expect the mean and standard deviation of the new sample to be the ones given above? The mean and standard deviation from a new sample are likely to be drastically different from those given above O No, the mean and standard deviation would not be the same, but should be close to those given above O Yes, the mean and standard deviation do not change just because of who we sampled S g) The sample means obtained are point estimates for the mean height of all active individuals, if the sample of individuals is equivalent to a simple random sample. What measure do we use to quantify the variability of such and estimate (Hint: recall that SE if o is unknown )? vn Compute this quantity using the data from the original sample under the condition that the data are from a simple random sample. SE (please round to four decimal places) n S

h) Treat the summary statistic values as population values. Find the probability that the mean height of the 507 individuals is greater than 172.1 cm? In other words, find P > 172.1). (please round to four decimal places) Treat the summary statistic values as population values. Find the probability that the mean height of another sample of 507 individuals is less than 170.3 cm? In other words, find PC < 170.3). (please round to four decimal places) Treat the summary statistic values as population values. Find the probability that the mean height of another sample of 507 individuals in between 170.6 cm and 171.7 cm? In other words, find P(170.6 < Ğ < 171.7).(please round to four decimal places)