       Re: Basic normal and t table questions

• To: mathgroup at smc.vnet.net
• Subject: [mg110054] Re: Basic normal and t table questions
• From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
• Date: Sun, 30 May 2010 23:46:56 -0400 (EDT)

```Hi Kurt

In:= Off[ Solve::"ifun" ]
sol = Solve[ (1 - CDF[NormalDistribution[0, 1], z]) == 0.025, z ][]

Out= {z -> 1.95996}

In:= z95 = z /. sol

Out= 1.95996

Thus:

In:= pValue2Sided = 2*(1 - CDF[NormalDistribution[0, 1], z95])

Out= 0.05

And:

In:= zScore = Quantile[ NormalDistribution[ 0, 1 ], pValue2Sided/2 ]
{zScore, -zScore}

Out= -1.95996

Out= {-1.95996, 1.95996}

In:= Off[ Solve::"ifun" ]
sol = Solve[ (1 - CDF[NormalDistribution[0, 1], z]) == 0.05, z ][]

Out= {z -> 1.64485}

In:= z90 = z /. sol

Out= 1.64485

Thus

In:= pValue2Sided = 2*(1 - CDF[NormalDistribution[0, 1], z90])

Out= 0.1

In:= zScore = Quantile[ NormalDistribution[ 0, 1 ], pValue2Sided/2 ]
{zScore, -zScore}

Out= -1.64485

Out= {-1.64485, 1.64485}

Cheers

Barrie

>>> On 30/05/2010 at 8:48 pm, in message <201005301048.GAA29139 at smc.vnet.net>,
Canopus56 <canopus56 at yahoo.com> wrote:
> I am taking an intro to stats class and am trying to learn some Mathematica
> functions related to basic statistics.
>
> I would like to use Mathematica to calculate exact values and inverse values
> from the standard normal table and Student's t distribution table.
>
> For example, the following returns the cdf equvialent to standard normal
> distribution table for a known mu, sigma (STD) and target x-bar:
>
> (1 - CDF[NormalDistribution[187000, 2181.9716], 190000])
>
> The following returns the two-sided t-distribution value for a known
> z-statistic:
>
> StudentTPValue[-0.1373, 6, TwoSided -> True]
>
> Q1) How do I get the inverse of these, which the equivalent of reading a cdf
> table and a t-distribution table backwards, i.e. -
>
> a) Given a cdf, how do I return the z-statistic from a standard normal
> distribution?
>
> b) Given a P-Value and sampling distribution size, how did I return the z-star
> critical test value?
>
> Thanks - Kurt

```

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