TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2023W/HW10.3
- One-sample test for proportions (without R)
In the context of the one-sample situation for proportions let the observed relative frequency be . Let the null hypothesis be and further let the (approximate) test be two-sided. Answer the following questions only using the table below, which shows the -quantiles of the -distribution.
a) What is the value of the question mark in the table?
b) For the null hypothesis is rejected on the 10%-level?
c) For the null hypothesis is rejected on the 3%-level?
0.01 | 0.05 | 0.1 | 0.2 | 0.5 | |
---|---|---|---|---|---|
-0.32 | 0.36 | 0.72 | 1.16 | ? |
Lösungsvorschlag von Friday[Bearbeiten | Quelltext bearbeiten]
--Friday Sa 30 Jan 2021 18:18:43 CET
a)[Bearbeiten | Quelltext bearbeiten]
The distribution has a mean of 2 and is symetric. Therefore the -quantile for must be .
b)[Bearbeiten | Quelltext bearbeiten]
While the table in the description certently is useful, it is not exactly what we need. First, there are the quantiles for the -distribution while we need the -distribution. Moreover we need the quantiles.
The adapted table for the -distribution looks like:
0.02 | 0.1 | 0.2 | 0.4 | 1 | |
---|---|---|---|---|---|
-2.32 | -1.64 | -1.28 | -0.84 | 0 |
Now we can test the hypothesis:
As , we do not reject on the 10%-level.
c)[Bearbeiten | Quelltext bearbeiten]
Although the table hasn't got the exact values for the 3% level, we can say that z is in the rejection region for the 2% level (-.32-2 = -2.32) so the H0 would be already rejected at this level and therfore would also be rejected at the 3% level (edited by M.T.)