91Ó°ÊÓ

The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. The "flipped" classroom is one where the content is delivered via video and watched at home, while class time is used for homework and activities. $$ \begin{array}{llllllll} \hline \text { Traditional } & 70.8 & 69.1 & 79.4 & 67.6 & 85.3 & 78.2 & 56.2 \\\ & 81.3 & 80.9 & 71.5 & 63.7 & 69.8 & 59.8 & \\ \hline \text { Fipped } & 76.4 & 71.6 & 63.4 & 72.4 & 77.9 & 91.8 & 78.9 \\ & 76.8 & 82.1 & 70.2 & 91.5 & 77.8 & 76.5 & \end{array} $$ (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? (b) Which course has more dispersion in exam scores using the standard deviation as the measure of dispersion? (c) Suppose the score of 59.8 in the traditional course was incorrectly recorded as \(598 .\) How does this affect the range? the standard deviation? What property does this illustrate?

One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2014 semester in a College Algebra class at Joliet Junior College. $$ Q_{1}=42 \quad Q_{2}=51.5 \quad Q_{3}=72.5 $$ (a) Provide an interpretation of these results. (b) Determine and interpret the interquartile range. (c) Suppose a student spent 2 hours doing homework for a section. Is this an outlier? (d) Do you believe that the distribution of time spent doing homework is skewed or symmetric? Why?

The acidity or alkalinity of a solution is measured using \(\mathrm{pH}\). A pH less than 7 is acidic, while a pH greater than 7 is alkaline. The following data represent the \(\mathrm{pH}\) in samples of bottled water and tap water. $$ \begin{array}{lllllll} \hline \text { Tap } & 7.64 & 7.45 & 7.47 & 7.50 & 7.68 & 7.69 \\ & 7.45 & 7.10 & 7.56 & 7.47 & 7.52 & 7.47 \\ \hline \text { Bottled } & 5.15 & 5.09 & 5.26 & 5.20 & 5.02 & 5.23 \\ & 5.28 & 5.26 & 5.13 & 5.26 & 5.21 & 5.24 \\ \hline \end{array} $$ (a) Which type of water has more dispersion in pH using the range as the measure of dispersion? (b) Which type of water has more dispersion in pH using the standard deviation as the measure of dispersion?

It is well documented that active maternal smoking during pregnancy is associated with lower-birth-weight babies. Researchers wanted to determine if there is a relationship between paternal smoking habits and birth weight. The researchers administered a questionnaire to each parent of newborn infants. One question asked whether the individual smoked regularly. Because the survey was administered within 15 days of birth, it was assumed that any regular smokers were also regular smokers during pregnancy. Birth weights for the babies (in grams) of nonsmoking mothers were obtained and divided into two groups, nonsmoking fathers and smoking fathers. The given data are representative of the data collected by the researchers. The researchers concluded that the birth weight of babies whose father smoked was less than the birth weight of babies whose father did not smoke. $$ \begin{array}{lll|lll} &{\text { Nonsmokers }} & &&{\text { Smokers }} \\ \hline 4194 & 3522 & 3454 & 3998 & 3455 & 3066 \\ \hline 3062 & 3771 & 3783 & 3150 & 2986 & 2918 \\ \hline 3544 & 3746 & 4019 & 4216 & 3502 & 3457 \\ \hline 4054 & 3518 & 3884 & 3493 & 3255 & 3234 \\ \hline 4248 & 3719 & 3668 & 2860 & 3282 & 2746 \\ \hline 3128 & 3290 & 3423 & 3686 & 2851 & 3145 \\ \hline 3471 & 4354 & 3544 & 3807 & 3548 & 4104 \\ \hline 3994 & 2976 & 4067 & 3963 & 3892 & 2768 \\ \hline 3732 & 3823 & 3302 & 3769 & 3509 & 3629 \\ \hline 3436 & 3976 & 3263 & 4131 & 3129 & 4263 \\ \hline \end{array} $$ (a) Is this an observational study or a designed experiment? Why? (b) What is the explanatory variable? What is the response variable? (c) Can you think of any lurking variables that may affect the results of the study? (d) In the article, the researchers stated that "birthweights were adjusted for possible confounders \(\ldots .\) "What does this mean? (e) Determine summary statistics (mean, median, standard deviation, quartiles) for each group. (f) Interpret the first quartile for both the nonsmoker and smoker group. (g) Draw a side-by-side box plot of the data. Does the side-byside boxplot confirm the conclusions of the study?

The data on the following page represent the pulse rates (beats per minute) of nine students enrolled in a section of Sullivan's course in Introductory Statistics. Treat the nine students as a population. $$ \begin{array}{lc} \text { Student } & \text { Pulse } \\ \hline \text { Perpectual Bempah } & 76 \\ \hline \text { Megan Brooks } & 60 \\ \hline \text { Jeff Honeycutt } & 60 \\ \hline \text { Clarice Jefferson } & 81 \\ \hline \text { Crystal Kurtenbach } & 72 \\ \hline \text { Janette Lantka } & 80 \\ \hline \text { Kevin MeCarthy } & 80 \\ \hline \text { Tammy Ohm } & 68 \\ \hline \text { Kathy Wojdyla } & 73 \end{array} $$ (a) Determine the population standard deviation. (b) Find three simple random samples of size 3 , and determine the sample standard deviation of each sample. (c) Which samples underestimate the population standard deviation? Which overestimate the population standard deviation?

The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the \(\mathrm{pH}\) in samples of bottled water and tap water. $$ \begin{array}{lllllll} \hline \text { Tap } & 7.64 & 7.45 & 7.47 & 7.50 & 7.68 & 7.69 \\ & 7.45 & 7.10 & 7.56 & 7.47 & 7.52 & 7.47 \\ \hline \text { Bottled } & 5.15 & 5.09 & 5.26 & 5.20 & 5.02 & 5.23 \\ & 5.28 & 5.26 & 5.13 & 5.26 & 5.21 & 5.24 \\ \hline \end{array} $$ (a) Determine the mean, median, and mode \(\mathrm{pH}\) for each type of water. Comment on the differences between the two water types. (b) Suppose the \(\mathrm{pH}\) of 7.10 in tap water was incorrectly recorded as \(1.70 .\) How does this affect the mean? the median? What property of the median does this illustrate?

The following data represent the pulse rates (beats per minute) of nine students enrolled in a section of Sullivan's Introductory Statistics course. Treat the nine students as a population. $$ \begin{array}{lc} \text { Student } & \text { Pulse } \\ \hline \text { Perpectual Bempah } & 76 \\ \hline \text { Megan Brooks } & 60 \\ \hline \text { Jeff Honeycutt } & 60 \\ \hline \text { Clarice Jefferson } & 81 \\ \hline \text { Crystal Kurtenbach } & 72 \\ \hline \text { Janette Lantka } & 80 \\ \hline \text { Kevin McCarthy } & 80 \\ \hline \text { Tammy Ohm } & 68 \\ \hline \text { Kathy Wojdyla } & 73 \\ \hline \end{array} $$ (a) Determine the population mean pulse. (b) Find three simple random samples of size 3 and determine the sample mean pulse of each sample. (c) Which samples result in a sample mean that overestimates the population mean? Which samples result in a sample mean that underestimates the population mean? Do any samples lead to a sample mean that equals the population mean?

Explain how to determine the shape of a distribution using the box plot and quartiles.

Ethan and Drew went on a 10 -day fishing trip. The number of smallmouth bass caught and released by the two boys each day was as follows: $$ \begin{array}{lrrrrrrrrrr} \hline \text { Ethan } & 9 & 24 & 8 & 9 & 5 & 8 & 9 & 10 & 8 & 10 \\ \hline \text { Drew } & 15 & 2 & 3 & 18 & 20 & 1 & 17 & 2 & 19 & 3 \\ \hline \end{array} $$ (a) Find the population mean and the range for the number of smallmouth bass caught per day by each fisherman. Do these values indicate any differences between the two fishermen's catches per day? Explain. (b) Draw a dot plot for Ethan. Draw a dot plot for Drew. Which fisherman seems more consistent? (c) Find the population standard deviation for the number of smallmouth bass caught per day by each fisherman. Do these values present a different story about the two fishermen's catches per day? Which fisherman has the more consistent record? Explain. (d) Discuss limitations of the range as a measure of dispersion.

The following data represent the weights (in grams) of a simple random sample of \(50 \mathrm{M} \& \mathrm{M}\) plain candies. $$ \begin{array}{lllllll} \hline 0.87 & 0.88 & 0.82 & 0.90 & 0.90 & 0.84 & 0.84 \\ \hline 0.91 & 0.94 & 0.86 & 0.86 & 0.86 & 0.88 & 0.87 \\ \hline 0.89 & 0.91 & 0.86 & 0.87 & 0.93 & 0.88 & \\ \hline 0.83 & 0.95 & 0.87 & 0.93 & 0.91 & 0.85 & \\ \hline 0.91 & 0.91 & 0.86 & 0.89 & 0.87 & 0.84 & \\ \hline 0.88 & 0.88 & 0.89 & 0.79 & 0.82 & 0.83 & \\ \hline 0.90 & 0.88 & 0.84 & 0.93 & 0.81 & 0.90 & \\ \hline 0.88 & 0.92 & 0.85 & 0.84 & 0.84 & 0.86 & \\ \hline \end{array} $$ Determine the shape of the distribution of weights of M\&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M\&M?