91Ó°ÊÓ

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint. $$ \begin{array}{lllll} 3.4 & 2.5 & 4.8 & 2.9 & 3.6 \\ 2.8 & 3.3 & 5.6 & 3.7 & 2.8 \\ 4.4 & 4.0 & 5.2 & 3.0 & 4.8 \end{array} $$ Assume that the measurements are a simple random sample. (a) What is the sample size for the above sample? (b) Calculate the sample mean for this data. (c) Calculate the sample median. (d) Plot the data by way of a dot plot. (e) Compute the \(20 \%\) trimmed mean for the above data set.

Twenty adult males between the ages of 30 and 40 were involved in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly selected to be a control group and ten others were assigned to take part in the regimen as the treatment group for a period of 6 months. The following data show the reduction in cholesterol experienced for the time period for the 20 subjects: $$ \begin{array}{lrrrrr} \text { Control group: } & 7 & 3 & -4 & 14 & 2 \\ & 5 & 22 & -7 & 9 & 5 \\ \text { Treatment group: } & -6 & 5 & 9 & 4 & 4 \\ & 12 & 37 & 5 & 3 & 3 \end{array} $$ (a) Do a dot plot of the data for both groups on the same graph. (b) Compute the mean, median, and \(10 \%\) trimmed means for both groups. (c) Explain why the difference in the mean suggests one conclusion about the effect of the regimen, while the difference in medians or trimmed means suggests a different conclusion.

A manufacturer of electronic components is interested in determining the lifetime of a certain type of battery. A sample, in hour's of life, is as follows: \(123,116,122,110,175,126,125,111,118,117 .\) (a) Find the sample mean and median. (b) What feature in this data set is responsible for the substantial difference between the two?

A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be \(570 \mathrm{~mm}\). The data are as follows: $$ 572,572,573,568,569,575,565,570 $$ (a) Find the sample mean and median. (b) Find the sample variance, standard deviation, and range. (c) Using the calculated statistics in parts (a) and (b), can you comment on the quality of the tires?

A study of the effects of smoking on sleep patterns is conducted. The measure observed is the time. in minutes, that it takes to fall asleep. These data are obtained: $$ \begin{array}{lllll} \text { Smokers: } & 69.3 & 56.0 & 22.1 & 47.6 \\ & 53.2 & 48.1 & 52.7 & 34.4 \\ & 60.2 & 43.8 & 23.2 & 13.8 \\ \text { Nonsmokers: } & 28.6 & 25.1 & 26.4 & 34.9 \\ & 29.8 & 28.4 & 38.5 & 30.2 \\ & 30.6 & 31.8 & 41.6 & 21.1 \\ & 36.0 & 37.9 & 13.9 & \end{array} $$ (a) Find the sample mean for each group. (b) Find the sample standard deviation for each group. (c) Make a dot plot of the data sets \(A\) and \(B\) on the same line. (d) Comment on what kind of impact smoking appears to have on the time required to fall asleep.

The following scores represent the final examination grade for an elementary statistics course: $$ \begin{array}{lllllllll} 23 & 60 & 79 & 32 & 57 & 74 & 52 & 70 & 82 \\ 36 & 80 & 77 & 81 & 95 & 41 & 65 & 92 & 85 \\ 55 & 76 & 52 & 10 & 64 & 75 & 78 & 25 & 80 \\ 98 & 81 & 67 & 41 & 71 & 83 & 54 & 64 & 72 \\ 88 & 62 & 74 & 43 & 60 & 78 & 89 & 76 & 84 \\ 48 & 84 & 90 & 15 & 79 & 34 & 67 & 17 & 82 \\ 69 & 74 & 63 & 80 & 85 & 61 & & & \end{array} $$ (a) Construct a stem-and-leaf plot for the examination grades in which the stems are \(1,2,3 \ldots . .9\). (b) Set up a relative frequency distribution. (c) Construct a relative frequency histogram, draw an estimate of the graph of the distribution and discuss the skewness of the distribution. (d) Compute the sample mean, sample median, and sample standard deviation.

The following data represent the length of life in years, measured to the nearest tenth, of 39 similar fuel pumps: $$ \begin{array}{rrrrrr} 2.0 & 3.0 & 0.3 & 3.3 & 1.3 & 0.4 \\ 0.2 & 6.0 & 5.5 & 6.5 & 0.2 & 2.3 \\ 1.5 & 4.0 & 5.9 & 1.8 & 4.7 & 0.7 \\ 4.5 & 0.3 & 1.5 & 0.5 & 2.5 & 5.0 \\ 1.0 & 6.0 & 5.6 & 6.0 & 1.2 & 0.2 \end{array} $$ (a) Construct a stem-and-leaf plot for the life in years of the fuel pump using the digit to the left of the decimal point as the stem for each observation. (b) Set up a relative frequency distribution. (c) Compute the sample mean, sample range, and sample standard deviation.

The nicotine contents, in milligrams, for 40 cigarettes of a certain brand were recorded as follows: $$ \begin{array}{rrrrr} 1.09 & 1.92 & 2.31 & 1.79 & 2.28 \\ 1.74 & 1.47 & 1.97 & 0.85 & 1.24 \\ 1.58 & 2.03 & 1.70 & 2.17 & 2.55 \\ 2.11 & 1.86 & 1.90 & 1.68 & 1.51 \\ 1.64 & 0.72 & 1.69 & 1.85 & 1.82 \\ 1.79 & 2.46 & 1.88 & 2.08 & 1.67 \\ 1.37 & 1.93 & 1.40 & 1.64 & 2.09 \\ 1.75 & 1.63 & 2.37 & 1.75 & 1.69 \end{array} $$ (a) Find the sample mean and sample median. (b) Find the sample standard deviation.

The following data are the measures of the diameters of 36 rivet heads in \(1 / 100\) of an inch. $$ \begin{array}{llllllll} 6.72 & 6.77 & 6.82 & 6.70 & 6.78 & 6.70 & 6.62 & 6.75 \\ 6.66 & 6.66 & 6.64 & 6.76 & 6.73 & 6.80 & 6.72 & 6.76 \\ 6.76 & 6.68 & 6.66 & 6.62 & 6.72 & 6.76 & 6.70 & 6.78 \\ 6.76 & 6.67 & 6.70 & 6.72 & 6.74 & 6.81 & 6.79 & 6.78 \\ 6.66 & 6.76 & 6.76 & 6.72 & & & & \end{array} $$ (a) Compute the sample mean and sample standard deviation. (b) Construct a relative frequency histogram of the data. (c) Comment on whether there is any clear indication or not that the sample came from a population that depicts a bell-shaped distribution.

The following are historical data on staff salaries (dollars per pupil on 30 schools sampled in the eastern part of the United States in the early \(1970 \mathrm{~s}\) ). $$ \begin{array}{llllllll} 3.79 & 2.99 & 2.77 & 2.91 & 3.10 & 1.84 & 2.52 & 3.22 \\ 2.45 & 2.14 & 2.67 & 2.52 & 2.71 & 2.75 & 3.57 & 3.85 \\ 3.36 & 2.05 & 2.89 & 2.83 & 3.13 & 2.44 & 2.10 & 3.71 \\ 3.14 & 3.54 & 2.37 & 2.68 & 3.51 & 3.37 & & \end{array} $$ (a) Compute the sample mean and sample standard deviation. (b) Construct a relative frequency histogram of the data. (c) Construct a stem-and-leaf display of the data.