Version | Date | Change | Details |
---|---|---|---|

1.00 | December 7, 2015 | Book added to the BC Open Textbook Collection | |

1.01 | June 6, 2019 | Updated the book's theme. | The styles of this book have been updated, which may affect the page numbers of the PDF and print copy. Added a Versioning History page. |

1.02 | June 23, 2020 | Updated the copyright information and front matter. | Listed the adapting author's name as an author, which was missing. Updated the copyright and publishing information and the front matter to conform with BCcampus style. Updated the book cover. |

- chi-square test and categorical variables
- null and alternative hypotheses for test of independence

- simple linear regression model
- least squares method
- coefficient of determination
- confidence interval for the average of the dependent variable
- prediction interval for a specific value of the dependent variable

Download for free from the B.C. Open Textbook Collection.

Mahbobi, M. & Tiemann, T. K. (2015). *Introductory Business Statistics with Interactive Spreadsheets*. Victoria, B.C.: BCcampus. https://opentextbc.ca/introductorybusinessstatistics/

Size |
Frequency |
---|---|

6 | 3 |

7 | 24 |

8 | 33 |

9 | 20 |

10 | 17 |

A |
B |
C |
D |
E |
---|---|---|---|---|

1 | 6 | 3 | 5.06 | 15.19 |

2 | 7 | 24 | 1.56 | 37.5 |

3 | 8 | 33 | 0.06 | 2.06 |

4 | 9 | 20 | 0.56 | 11.25 |

5 | 10 | 17 | 3.06 | 52.06 |

6 | n= |
97 | Var = 1.217139 | |

7 | Std.dev = 1.103.24 |

Proportion below |
.75 | .90 | .95 | .975 | .99 | .995 |
---|---|---|---|---|---|---|

z-score |
.674 | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |

df |
prob = .10 |
prob = .05 |
prob - .025 |
prob = .01 |
prob = .005 |
---|---|---|---|---|---|

1 | 3.078 | 6.314 | 12.70 | 13.81 | 63.65 |

5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 |

6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 |

7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 |

8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 |

9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 |

10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 |

20 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 |

30 | 1.310 | 1.697 | 2.046 | 2.457 | 2.750 |

40 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 |

Infinity | 1.282 | 1.645 | 1.960 | 2.326 | 2.58 |

- Many things are distributed the same way, at least once we’ve standardized the members’ values into z-scores.
- The central limit theorem gives users of statistics a lot of useful information about how the sampling distribution of
*x*is related to the original population of*x*’s. - The t-distribution lets us do many of the things the central limit theorem permits, even when the variance of the population,
*s*, is not known._{x}

alpha | .1 | .05 | .03 | .01 |
---|---|---|---|---|

df infinity | 1.28 | 1.65 | 1.96 | 2.33 |

Size | Frequency | Relative Frequency |
---|---|---|

6 | 3 | .031 |

7 | 24 | .247 |

8 | 33 | .340 |

9 | 20 | .206 |

10 | 17 | .175 |

Size | Relative Frequency |
---|---|

6 | .06 |

7 | .13 |

8 | .22 |

9 | .3 |

10 | .26 |

11 | .03 |

Sock Size | Frequency in Sample | Population Relative Frequency | Expected Frequency = 97*C | (O-E)^2/E |
---|---|---|---|---|

6 | 3 | .06 | 5.82 | 1.3663918 |

7 | 24 | .13 | 12.61 | 10.288033 |

8 | 33 | .22 | 21.34 | 6.3709278 |

9 | 20 | .3 | 29.1 | 2.8457045 |

10 | 17 | .26 | 25.22 | 2.6791594 |

11 | 0 | .03 | 2.91 | 2.91 |

97 | χ = 26.460217^{2} |

Orders |
||||||

Fish |
Veggie |
Steak |
Spaghetti |
Total |
||

Age Groups |
Kids |
26 | 21 | 15 | 20 | 82 |

Adults |
100 | 74 | 60 | 70 | 304 | |

Seniors |
90 | 45 | 80 | 110 | 325 | |

Total |
216 | 140 | 155 | 200 | 711 |

Orders |
||||||
---|---|---|---|---|---|---|

Fish |
Veggie |
Steak |
Spaghetti |
Total |
||

Age Groups |
Kids |
24.95 | 16.15 | 17.88 | 23.07 | 82 |

Adults |
92.35 | 59.86 | 66.27 | 85.51 | 304 | |

Seniors |
98.73 | 63.99 | 70.85 | 91.42 | 325 | |

Total |
216 | 140 | 155 | 200 | 711 |

Worker |
Wage (dollars/hour) |
---|---|

Smith | 12.65 |

Wilson | 12.67 |

Peterson | 11.9 |

Jones | 10.45 |

Gordon | 13.5 |

McCoy | 12.95 |

Bland | 11.77 |

Hypothesis test: Mean |

Null hypothesis: Mean = $11.71 |

Alternative: greater than |

Computed t statistic = 1.48 |

p-value = .094 |

Table 5.3 The SAS System Software Output for Dr. Alston’s Grade Study | ||||||

TTFST Procedure |
||||||

Variable: GRADE | ||||||

Dept |
N |
Mean |
Dev |
Std Error |
Minimum |
Maximum |

Econ | 38 | 2.28947 | 1.01096 | .16400 | 0 | 4.00000 |

Variance |
t |
df |
Prob>[t] |

Unequal | -2.3858 | 85.1 | .0193 |

Equal | -2.3345 | 87.0 | .0219 |

For H: Variances are equal, f=1.35, df[58.37], Prob>f=.3485_{o} |

Team leader |
Output—cool day |
Output—hot day |
Difference (cool-hot) |
---|---|---|---|

November 14 | July 20 | ||

Martinez | 153 | 149 | 4 |

McAlan | 167 | 170 | -3 |

Wilson | 164 | 155 | 9 |

Burningtree | 183 | 179 | 4 |

Sanchez | 177 | 167 | 10 |

Lilly | 162 | 150 | 12 |

Cantu | 165 | 158 | 7 |

Row |
Cities |
Populations |
Locations |
Ranks |
---|---|---|---|---|

1 | St. Albert, AB | 64,377 | West | 1 |

2 | Strathcona County, AB | 98,232 | West | 2 |

3 | Boucherville, QC | 41,928 | East | 6 |

4 | Lacombe, AB | 12,510 | West | 17 |

5 | Rimouski, QC | 53,000 | East | 18 |

6 | Repentigny, QC | 85,425 | East | 20 |

7 | Blainville, QC | 57,058 | East | 21 |

8 | Fredericton, NB | 99,066 | East | 22 |

9 | Stratford, ON | 32,217 | East | 23 |

10 | Aurora, ON | 56,697 | East | 24 |

11 | North Vancouver, B.C. (District Municipality) | 88,085 | West | 25 |

12 | North Vancouver, B.C. (City) | 51,650 | West | 28 |

13 | Halton Hills, ON | 62,493 | East | 29 |

14 | Newmarket, ON | 84,902 | East | 31 |

15 | Red Deer, AB | 96,650 | West | 33 |

16 | West Vancouver, B.C. | 44,226 | West | 36 |

17 | Brossard, QC | 83,800 | East | 38 |

18 | Camrose, AB | 18,435 | West | 40 |

One-Tail Significance |
.05 | .025 | .01 |

Two-Tail Significance |
.1 | .05 | .02 |

Number of Pairs, N |
|||

5 | 0 | ||

6 | 2 | 0 | |

7 | 3 | 2 | 0 |

8 | 5 | 3 | 1 |

9 | 8 | 5 | 3 |

10 | 10 | 8 | 5 |

Attribute |
Mean: Student Rating |
Mean: Big Firm Rating |
---|---|---|

High Accounting GPA | 2.06 | 2.56 |

High Overall GPA | .08 | -.08 |

Communication Skills | 4.15 | 4.25 |

Personal Integrity | 4.27 | 7.5 |

Energy, drive, enthusiasm | 4.82 | 3.15 |

Appearance | 2.68 | 2.31 |

Data source: Baker and McGregor |

Attribute |
Mean Student Rating |
Mean Big Firm Rating |
Difference |
Rank |

High Accounting GPA | 2.06 | 2.56 | -.5 | -4 |

High Overall GPA | .08 | -.08 | .16 | 2 |

Communication Skills | 4.15 | 4.25 | -.1 | -1 |

Personal Integrity | 4.27 | 7.5 | -2.75 | -6 |

Energy, drive, enthusiasm | 4.82 | 3.15 | 1.67 | 5 |

Appearance | 2.68 | 2.31 | .37 | 3 |

sum of positive ranks = 2+5+3=10 | ||||

sum of negative ranks = 4+1+6=11 | ||||

number of pairs=6 |

Flavouring |
Expert Ranking |
Consumer Ranking |
---|---|---|

NYS21 | 7 | 8 |

K73 | 4 | 3 |

K88 | 1 | 4 |

Ba4 | 8 | 6 |

Bc11 | 2 | 5 |

McA A | 3 | 1 |

McA A | 9 | 9 |

WIS 4 | 5 | 2 |

WIS 43 | 6 | 7 |

n |
α=.05 |
α=.025 |
α=.10 |
---|---|---|---|

5 | .9 | ||

6 | .829 | .886 | .943 |

7 | .714 | .786 | .893 |

8 | .643 | .738 | .833 |

9 | .6 | .683 | .783 |

10 | .564 | .648 | .745 |

11 | .523 | .623 | .736 |

12 | .497 | .591 | .703 |

Flavouring |
Expert ranking |
Consumer ranking |
Difference |
d² |

NYS21 | 7 | 8 | -1 | 1 |

K73 | 4 | 3 | 1 | 1 |

K88 | 1 | 4 | -3 | 9 |

Ba4 | 8 | 6 | 2 | 4 |

Bc11 | 2 | 5 | -3 | 9 |

McA A | 3 | 1 | 2 | 4 |

McA A | 9 | 9 | 0 | 0 |

WIS 4 | 5 | 2 | 3 | 9 |

WIS 43 | 6 | 7 | -1 | 1 |

Sum |
38 |

y = price of apartments in $1000
x = distance of each apartment from downtown in kilometres
_{1}x = size of the apartment in square feet_{2} |
||

y |
x_{1} |
x_{2} |

55 | 1.5 | 350 |

51 | 3 | 450 |

60 | 1.75 | 300 |

75 | 1 | 450 |

55.5 | 3.1 | 385 |

49 | 1.6 | 210 |

65 | 2.3 | 380 |

61.5 | 2 | 600 |

55 | 4 | 450 |

45 | 5 | 325 |

75 | 0.65 | 424 |

65 | 2 | 285 |