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Mann-Introductory Statistics, Fifth Edition, Students Solutions Manual
1.1The word ‘statistics’ has the following two meanings:
- First, it refers to numerical facts such as the ages of persons, incomes of families, etc.
ii.Second, it refers to the field of study. It provides us with techniques that help us to collect, analyze, present, and interpret data and to make decisions.
1.3Population: All elements whose characteristics are being studied.
Sample: A portion of the population selected for a study.
Representative sample: A sample that possesses the characteristics of the population as closely as possible.
Random sample: A sample drawn in such a way that each element of the population has some chance of being included in the sample.
Sampling with replacement: A sampling procedure in which the item selected at each selection is put back in the population before the next item is drawn.
Sampling without replacement: A sampling procedure in which the item selected at each selection is not replaced in the population.
1.5A census is a survey that includes all members of the population. A survey based on a portion of the population is called a sample survey. A sample survey is preferred over a census for the following reasons:
- Conducting a census is very expensive because the size of the population is usually very large.
ii. Conducting a census is very time consuming.
iii.In many cases it is almost impossible to identify every member of the target population.
1.7a. Population b. Sample c. Populationd. Samplee. Population
1.9Member: Each city included in the table.
Variable: Number of dog bites reported.
Measurement: Dog bites in a specific city. For example, Oakdale’s 12 dog bites is a measurement.
Data set: Collection of dog bite numbers for the six cities listed in the table.
1.11a.Dog Bitesb. Six observations c. Six elements (cities)
1.13a. Quantitative variable: A variable that can assume numerical values.
- Qualitative variable: A variable that cannot be measured numerically but can be divided into different categories.
- Discrete variable: A variable whose values are countable.
- Continuous variable: A variable that can assume any value over a certain interval or intervals.
- Quantitative data: Data collected on a quantitative variable.
- Qualitative data: Data collected on a qualitative variable.
1.15a. Quantitative b. Quantitativec. Qualitative d. Quantitative e. Quantitative
1.17a. Discreteb. Continuousd. Discretee. Continuous
1.19Excel: In the first column type in Name and press ENTER, type in JACK and press ENTER, and repeat until all five names are listed. Then use the arrow keys or the mouse to move to the top of the second column. Type in Height(cm) and press ENTER, type in 165 and press ENTER, and repeat until all of the numbers are listed.
Note:To format the table like the textbook: Highlight the tops row and right click the mouse, selecting format cells, near the top of the pop up box select Borders. Then about a third of the way down on the left side of the box it says Border, under the word Border click on the box with the dark line on top of the box and then click on the box with the dark line on the bottom of the box. And then click on OK. To put in the line at the bottom of the table repeat these steps but do not click on the box with the dark line on top – just the one with the dark line on the bottom.
MINITABType the labels Name and Height (cm) in the grey row between the down arrow and 1. In the first row type Jack and press ENTER and repeat for all of the other names in the list. Use the mouse or the right arrow to move top of the second column. Enter each number and press ENTER.
1.21Internal sources of data are a company’s own files and records.
External sources of data are the sources that do not belong to a company.
1.23 a. Cross-section datab. Cross-section datac. Time-series datad. Time-series data
1.25
m / f / M2 / Mf / m2 f3 / 16 / 9 / 48 / 144
6 / 11 / 36 / 66 / 396
25 / 16 / 625 / 400 / 10,000
12 / 8 / 144 / 96 / 1152
15 / 4 / 225 / 60 / 900
18 / 14 / 324 / 252 / 4536
Sum= 79 / 69 / 1363 / 992 / 17,128
a. f = 69 b.m2 = 1363 c. mf = 992 d. m2f= 17,128
TI-83: Insert numbers as two lisst and then do the calculations as follows: press the 2nd key, then STAT, use the arrows to move over to MATH, use the arrows to move down to 5 sum or by pressing the number 5 key, and press ENTER. To sum the list in column L1 next press the 2nd key, the number 1 key, and then entering ) followed by ENTER. If you wish to sum the list in the second column do all of the above except this time press the number 2 key instead of the number 1 key. To do additional math before the summation just include the multiplication or press the key to square a number before entering the right parenthesis. The results here look only slightly different than those shown above.
Sum (L1) / Sum (L1 * L2)79 / 992
Sum (L2) / Sum (L1 2 * L2)
69 / 17128
Sum (L1 2)
1363
MINITAB: Enter the data for m and f into columns C1 and C2 with the labels m and f in the gray row just below the column numbers. Now select Calc and then Column Statistics causing a pop-up-box to open.Under the word Statistic is Sum and click on the box to the left of it and in the space beside the words Input variable type in the column to be added up which in this case is m. To sum the squares instead of clicking beside the word sum, this time click to the left of the words Sum of Squares which is near the top of the second column and in the box replace m with f.
To calculate Σmf select Calc and then Calculator which brings up the pop-up-box. Under the word “Expression” type in C1* C2 and in the box beside “store result in variable” type C3. Label this column mf. Do the same forΣm2f except type the expression as C1*C1*C2 its stored in C4, and labeled mmf. Then total the columns as you did for m and f.
Excel: Enter the data in two columns and at the top of each column be sure to label them. In an empty cell type =SUM(cell names) and press ENTER. Here I used column cfor fso its =SUM(c2:c7) and ENTER. To get the sum of the squares for m, insert the formula =SUMSQ(cell range) which in this example is =SUMSQ(B2:B7). To calculate the sum of the product of m*f enter the formula =SUMPRODUCT(cell range 1,cell range 2) and in this example it becomes =SUMPRODUCT(B2:B7,C2:C7). To get the sum of m2f enter the formula =SUMPRODUCT(cell range 1, cell range 1, cell range 2) which in this example is =SUMPRODUCT(B2:B7,B2:B7,C2:C7). Notethat all of these formulas can be found by selecting Insert, Function, and scrolling down until the function name appears in the box. Then all you need to do is enter the appropriate cell ranges. The second image here, presents the results when following the instruction on page 24 of the textbook which are slightly different than those presented here.
1.27
x / y / xy / x2 / y24 / 12 / 48 / 16 / 144
18 / 5 / 90 / 324 / 25
25 / 14 / 350 / 625 / 196
9 / 7 / 63 / 81 / 49
12 / 12 / 144 / 144 / 144
20 / 8 / 160 / 400 / 64
x = 88 / y =58 / xy = 855 / x2 = 1590 / y2 = 622
a. x = 88 b. y =58 c. xy = 855 d. x2 = 1590 e. y2 = 622
1.29a. y = 83 + 205 + 57 + 134 = $479b. (y)2 = (479)2 = 229,441
c. y2= (83)2 + (205)2 + (57)2 + (134)2 = 70,119
1.31a. x= 7 + 39 + 21 + 16 + 3 + 43 + 19 = 148 studentsb. (x)2 = (148) 2 = 21,904
c. x2= (7)2 + (39) 2 + (21)2 + (16)2 + (3)2 + (43)2 + (19) 2 = 4486 students
1.33Variable: The number of U.S. babies born as triplets and larger sets.
Measurement: The number of U.S. babies born as triplets and larger sets for a specific year.
Data Set: Collection of the number of U.S. babies born as triplets and larger sets for the years listed in the table.
1.35a.Sampleb. Population for the yearc. Sample d. Population
1.37a.Sampling without replacement, because once a patient is selected, he/she will not be replaced before the next patient is selected. All 10 selected patients must be different.
b.Sampling with replacement because both times the selection is made from the same group (consisting of all professors).
1.39 a.x = 8 + 14 + 3 + 7 + 10 + 5= 47 shoe pairsb. (x)2 = (47)2 = 2209
c.x2 = (8) 2 + (14) 2 + (3) 2 + (7) 2 + (10) 2 + (5) 2 = 443 shoes
1.41
m / f / f2 / mf / m2f / m23 / 7 / 49 / 21 / 63 / 9
16 / 32 / 1024 / 512 / 8192 / 256
11 / 17 / 289 / 187 / 2057 / 121
9 / 12 / 144 / 108 / 972 / 81
20 / 34 / 1156 / 680 / 13,600 / 400
Sum= 59 / 102 / 2662 / 1508 / 24,884 / 867
a. m = 59b. f2 = 2662c. mf = 1508d. m2f = 24,884e. m2 = 867
Self-Review Test for Chapter One
1.b2.c
3.a. A sample without replacement b. A sample with replacement
4.a. Qualitative b. Quantitative; continuousc. Quantitative; discreted. Quantitative; continuous
5.Member: A specific job included in the table. For example, Coach is a member.
Variable: Votes for the best job at the Superbowl.
Measurement: Votes for a specific Superbowl job. For example, Coach received 1,927 votes is a measurement.
Data set: The collection of votes for the five Superbowl jobs listed in the table.
- a. x = 8 + 5 + 10 + 6 + 5 + 8 = 42 roomsb. (x)2 = (42)2 =1764
c.x2 = (8)2 + (5)2 + (10)2 + (6)2 + (5)2 + (8)2 = 314
7.
m / f / m2 / mf / m2f / f 23 / 15 / 9 / 45 / 135 / 225
6 / 25 / 36 / 150 / 900 / 625
9 / 40 / 81 / 360 / 3240 / 1600
12 / 20 / 144 / 240 / 2880 / 400
15 / 12 / 225 / 180 / 2700 / 144
m = 45 / f = 112 / m2 = 495 / mf = 975 / m2f = 9855 / f 2 = 2994
a. m = 45 b. f = 112c. m2 = 495 d. mf = 975e. m2f = 9855f. f2 = 2994