MS 150 Quiz 12 Testing two sample means 11.2 • Name:

With the introduction of Microsoft Windows Vista edition and Microsoft Office 2007, Microsoft has effectively replaced Arial as the default sans-serif font with Calibri. Calibri is based on ten years of research on reading and the development of subpixel rendering technologies.

One impact of Microsoft's research is that Calibri is actually slightly smaller visually than Arial. This means more words can fit in a single sentence. Which means a two page double spaced expository writing essay written using Calibri may require more words.

The texts below were original set so that the line length was identical in 12 point Arial and Calibri using a word processor with identical margins for both fonts. To facilitate printing on this quiz, the lines were indented an inch to create room for the character count column.

Test the hypothesis that a student will have to write more words to fill up a two page paper. Run a two tailed t-test for independent samples to determine if the number of letters per line differs for Arial and Calibri.

CharsArial Lines
60Contemporary sans serif design, Arial contains more humanist
73characteristics than many of its predecessors and as such is more in tune
72with the mood of the last decades of the twentieth century. The overall
75treatment of curves is softer and fuller than in most industrial style sans
74serif faces. Terminal strokes are cut on the diagonal which helps to give
70the face a less mechanical appearance. Arial is an extremely versatile
73family of typefaces which can be used with equal success for text setting
64in reports, presentations, magazines etc, and for display use in
69newspapers, advertising and promotions. Features: Arial contains 1674
71glyphs and 909 standard kern pairs. This font does not include embedded
71bitmaps. Font designer: Monotype Type Drawing Office - Robin Nicholas,
69Patricia Saunders 1982. Typeface © The Monotype Corporation plc. Data
72© The Monotype Corporation plc/Type Solutions Inc. 1990-1992. All Rights
69Reserved. Arial® Trademark of The Monotype Corporation plc registered
  1. _________ Calculate the sample size nx for the number of lines of Arial.
  2. _________ Calculate the sample mean x number of characters per line (Chars) for Arial.
  3. _________ Calculate the sample standard deviation sx for the number of characters per line for Arial.
CharsCalibri Lines
81Calibri is a modern sans serif family with subtle roundings on stems and corners.
80It features real italics, small caps, and multiple numeral sets. Its proportions
82allow high impact in tightly set lines of big and small text alike. Calibri's many
79curves and the new rasteriser team up in bigger sizes to reveal a warm and soft
80character. Features: Calibri contains 1121 glyphs and 14148 standard kern pairs,
73see below for OpenType kern pair information. This font includes embedded
76bitmaps. Font designer: Luc(as) de Groot. © 2006 Microsoft Corporation. All
75Rights Reserved. Calibri is either a registered trademark or a trademark of
84Microsoft Corporation in the United States and/or other countries. End of line fill.
  1. _________ Calculate the sample size ny for the number of lines of Calibri.
  2. _________ Calculate the sample mean y number of characters per line for Calibri.
  3. _________ Calculate the sample standard deviation sy for the number of characters per line for Calibri.
  4. _________ Calculate the the difference between two sample means xd.
  5. _________ Are the sample means for the two fonts mathematically different?
  6. _________ Calculate the degrees of freedom using the smaller of the two sample sizes.
  7. _________ Calculate the tcritical using alpha α = 0.05 and the degrees of freedom.
  8. _________ Calculate the standard error SE for two independent samples.
  9. _________ Calculate the margin of error E for two independent samples.
  10. Determine the 95% confidence interval for the population mean difference μd

    ____________ < μd < _____________
  11. _________ Does the confidence interval include a mean difference of zero?
  12. _________ Is the mean number of characters per line statistically significantly different at a risk of a type I error alpha α = 0.05?
  13. __________________ Would we "fail to reject" or "reject" a null hypothesis of no difference in the mean number of characters?
  14. __________________ What is the p-value?
  15. __________________ What is the maximum level of confidence we can have that the difference is statistically significant?
  16. __________________ Will you have to type more words in Calibri than in Arial to fill up a two page essay?
Hypothesis testing and confidence intervals for two independent samples
Statistic or ParameterSymbolEquationsOpenOffice
Degrees of freedom (approx.)df[smaller sample n] − 1=COUNT(smaller sample)-1
Calculate t-critical for a two-tailed test tc=TINV(α;df)
Calculate the standard error SE for two independent samples SE standard error for two sample means =sqrt((sx^2/nx)+(sy^2/ny))
Calculate a margin of error E for two independent samples using tcritical and the standard error SE. E margin_error (1K) =tc*SE
Calculate the difference between two sample means xd xy =average(data set x)-average(data set y)
Calculate a confidence interval for a population mean difference μd from a sample mean difference xd and a margin of error E xd − E < μd < xd + E
Calculate a p-value for the difference of the means for two independent samples where the population standard deviations are unknown =TTEST(x data;y data;2;3)

The new fonts display well only on machines that are tuned for ClearType. Windows XP is not tuned for ClearType out of the box and the new fonts look terrible on Windows XP or any earlier operating system. Microsoft does provide a ClearType tuning power toy for Windows XP as of 2007, and this can be used to properly render the new fonts. Another subtle change is that the automatic default point size is now 11 instead of 10. The fonts are hinted fonts and some like Consolas are far superior at the targeted 11 point size. This uptick in point size compensates to some extent for the smaller x-height, but at 12 point "expository paper standard size" the fonts appear to average more words per line.

Links to more information on the new fonts:
New Vista Fonts and the Web
A comprehensive look at the new Microsoft fonts
Vista Fonts
The Next Big Thing in Online Type
Downloading and Using Vista Web Fonts
The end of an era for Times New Roman
Common fonts to all versions of Windows & Mac equivalents
Segoe UI
New "C" fonts include interrobang character ‽

The science behind the font introductions

The Science of Word Recognition
The Magic of Reading: OSPREY, a technology to make computer screens readable