We have studied 2 different test statistics, z, and X2. Explain the similarities in; 1. How e

Lymnmeatlypamgfm

Lymnmeatlypamgfm

Answered question

2022-04-22

We have studied 2 different test statistics, z, and X2. Explain the similarities in;
1. How each test statistic is calculated
2. How each test statistic is used to determine if the sample statistic provides enough evidence against the null hypothesis to reject it.
*i saw another answer on here but it didn't go in depth so im still confused

Answer & Explanation

Derick Alvarado

Derick Alvarado

Beginner2022-04-23Added 10 answers

1.The z-test statistic for independent proportions and the chi-square test statistic are related to each other in such a way that the square of the z-test statistic is equal to the chi-square test statistic. That is,
(z2)=χ2
Both the test statistics are calculated for qualitative variables.
The z-test statistic can be calculated as;
z=pp0P0(1p0)n
Here,
p is the sample propotion
p0 is the population propotion
n is the sample size
The chi-square test statistic is,
χ2=(OE)2E
Here,
O is the observed frequency
E is the expected frequency
The chi-square test statistic is derived using the z-test statistic for proportion.
In order to determine whether the sample statistic provides enough evidence against the null hypothesis to reject it or not, the degrees of freedom are required to obtain for both the test.
The similarities between them, at 0.05 significance level, is
For df = k – 1 = 2 – 1, the critical value for chi-square is 3.84 which is the square of the critical z-value, that is, 1.96 at 5% level of significance. That is,
(Zα2)2=χ{α.1}2
Decision for rejecting the null hypothesis:
Reject H0 if χ23.84 or Z1.96, respectively, for chi-square and the z-test for proportions.

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