The observations given below are related with duration between two

vetrila10

vetrila10

Answered question

2021-11-26

The observations given below are related with duration between two patients that come to ER service of certain hospital. There is a claim that the distribution of durations is Exponential with V(X)=1.778. Evaluate the claim.
3.2644.620.4390.131.9751.2710.820.421.1450.612.4080.871.9420.320.620.3750.3832.5121.923.192.123.89

Answer & Explanation

Steven Arredondo

Steven Arredondo

Beginner2021-11-27Added 18 answers

Step 1
Under null hypothesis H0: The distributions between two patients follow exponential distribution with mean 1.778
μ=1λ=1.778
Under alternate hypothesis H1: The distributions between two patients do not follow exponential distribution of which mean is 1.778
μ=1λ1.778
Step 2
Sample Mean:
x=xin
=35.24422
=1.602
Exponential distribution has mean and standard deviation μ=1λ and σx=1λ2
Using central limit theorem,
XN(1λ,1λ2)
Step 3
Test statistic:
z=X1λ1λ2
=1.6021.778111.7782
=1.6021.7781.7782
0.09899
Computation of P-value:
The P-value for the two tailed z-value test is 0.9211 which can be obtained using the excel formula, "=2*NORM.S.DIST(-0.09899,TRUE)".
Step 4
Decision rule:
If pvalueα, then reject the null hypothesis.
Otherwise, do not reject the null hypothesis.
Conclusion:
Consider level of significance as 0.05.
The p-value is greater than level of significance.
Hence, we have insufficient evidence to reject null hypothesis and thus conclude that the duration between two patients that come to ER service of certain hospital follow exponential distribution with mean 1.778.

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