T-TEST ... how to write?

Questions
1

Some bus lines urban transport during rush hour average speed of 8 km / h.
Consideration was given to whether the route change would lead to a change in the average speed. The new route was therefore
passed with ten randomly selected days and showed that the average speed: 7.8 7.9 9.0
7.8 8.0 7.8 8.5 8.2 8.2 9.3. Decide whether the route change leads to changes in average speed.
We assume a normal distribution, and ? = 0.05.

data = {7.8, 7.9, 9, 7.8, 8, 7.8, 8.5, 8.2, 8.2, 9.3};

zaklad = 8;

n = Length[data];

hladina = 0.05 (*Signifiti level*)

Needs["HypothesisTesting`"]

mi = Mean[data];

sigma2 = Variance[data];

sigma = Sqrt[sigma2];

Kriterium = (Abs[zaklad - mi]*N[Sqrt[n]])/sigma

But I do not know how to make a t-test. Thank you for the advice :slight_smile:

2

Dear Martin,

The solution is simply

TTest[data,zaklad,SignificanceLevel->0.05]

to get the p-value or

TTest[data, zaklad, "TestConclusion", SignificanceLevel -> 0.05]

to get the conclusion:

The null hypothesis that the mean of the population is equal to 8 is not rejected at the 5. percent level based on the T test.

For more details please refer to: TTest—Wolfram Documentation

If you want to perform the test yourself, it is required that you count the test statistic and compare it to the quantile of the t-distribution corresponding to the \alpha =0.5 critical values.

data = {7.8, 7.9, 9, 7.8, 8, 7.8, 8.5, 8.2, 8.2, 9.3};
zaklad = 8;
hladina = 0.05;
n = Length[data];
mi = Mean[data];
sigma = StandardDeviation[data];
t = (mi - zaklad) Sqrt[n]/sigma;
qt = Quantile[StudentTDistribution[n - 1], 1 - hladina/2];
If[Abs[t] < 
  qt, "No basis to reject the H0: mi=zaklad", "Reject the hypothesis H0: mi=zaklad"]
3

Thank you :slight_smile: