The R commands shown below can be found here: zTable.R # The z-distribution # # R’s function ’pnorm’ calculates the area under the normal distribution # below a z-score. The area to the RIGHT of a z-score = 1 – the area to the LEFT of the z-score Title Imagine a group of 200 applicants who took a math test. Get Started. Participants are randomly selected 3. Step 1: Convert X to z-Score Z-SCORES 42 2.00 15 30 15 130 100 V X P z Figure A.2 shows the t distribution with 1 df. Remember that the table entries are the area under the standard normal curve to the left of z. BBB 1 1 s84 1683 1.682 1 SSI IBBO 1679 1679 1678 1877 1.677 1676 12706 4.303 2776 2.571 2447 2 306 2262 2228 z 201 2179 2.160 2 14S 2131 2.120 2110 2 2086 2080 2074 2069 2.064 2 060 2 oss 2 oS2 2 1 s t kT ()2 1 1 1 − −z Tz 6. -Transform pair Table • The inverse z-transform equation is complicated. Entries represent the area under the standardized normal distribution from - to z, Pr(Z1 3) −𝑢ὐ− −1ὑ 1 1− −1 <1 4) 𝛿ὐ − ὑ − ≠0 if >0 p(X < 130) = ? Appendix E, Table I (Or see Hays, p. 924) reports the cumulative normal probabilities for normally distributed variables in standardized form (i.e. The DV is measured on an interval scale 2. ’pnorm’ converts z-scores to areas, and ’qnorm’ converts areas to z-scores. It gives the probability that a standard normal random variable, Z, will not exceed a given number, z. Equivalently, it gives the probability that any normal random variable will not exceed a value more than a given number of standard deviations above its mean. Convert the Raw Score to a Z-score s z =X−X 15 z =130−100 15 z =30 z =2 Look up the proportion in the z-score table • The diagram shows that we are interested in the area above 130 (shaded). Assumppyp gtions of Hypothesis Testing 1. Find positive Z scores in this table. z 0.000 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291 0% 50% 60% 70% 80% 90% 95% 98% 99% 99.8% 99.9% Confidence Level t-table.xls 7/14/2007. z 820 z 132 2 1 ass 1860 1.833 1812 1736 1782 1771 1761 17S3 1.746 1740 1734 1729 1725 1721 1717 1714 1711 1706 1.703 1701 1.636 1 sal 1690 1688 1887 1. Page 1 of 1 of C:\data\StatPrimer\z-two-tails.doc Last printed 4/7/2007 10:47:00 AM Two tails of Z Entries in the table represent two-tailed P values for z statistics hundredths Powered by Create your own unique website with customizable templates. ansi z1.4-1993, table i, sample size code letters special levels general levels lot size shipping s-1 s-2 s-3 s-4 i ii ansi z1.4-1993, table iii-a, aql s for double normal procedure b a iii c a a a. title: ansi 1.4-1993.xls author: mwab created date: Note that the probabilities given in this table represent the area to the LEFT of the z-score. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. The table shows the right-hand “critical value” of t needed to obtain a given one-tailed probability (˛) in the right-hand tail (Table A.2). To find the area, you need to integrate.

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