Summary
Here’s a flowchart to illustrate the steps for conducting a hypothesis testing:
flowchart
subgraph hypothesis["(1) Hypothesis Testing"]
n1["1) State the null hypothesis H₀ and alternate hypothesis H₁"]
end
subgraph significancelevel[" (2) Significance Level"]
n2["2) Write down the level of significance, α (usually given)"]
end
subgraph statistics["(3) Test Statistics, under H₀"]
n3["3) Decide on the test statistic to be used and determine its distribution
For H2 Maths, this is usually Xbar"] nd["Use sampling theory to find or estimate the sampling distribution of Xbar"] end subgraph calculations["(4) Calculations"] n4["* Collect samples, calculate test (statistics) value"] n5["* Use the GC to calculate the p-value"] end subgraph conclusion["(5) Conclusion"] n6{"Is the test value ..."} n7["'flucuating normally?'
p-value more than α
or test value not in critical region
"] n8["'too rare an occasion?'
p-value less than or equal to α
or test value within critical region"] n9["Reject H₀:
i.e surely obtaining the test value,
if it follows the test statistics under H₀ ,
is too rare an occasion that H₀ must be false."] n10["Do not reject null H₀;
i.e the test value flucuate quite 'normally',
all within the tolerence of the significant level,
so it is not a surprise its distribution is the test statistics under H₀"] end hypothesis --> significancelevel significancelevel --> statistics statistics --> calculations calculations --> conclusion n6 --> n7 & n8 n7 --> n10 n8 --> n9 n4 --> n5 n3 --> nd
For H2 Maths, this is usually Xbar"] nd["Use sampling theory to find or estimate the sampling distribution of Xbar"] end subgraph calculations["(4) Calculations"] n4["* Collect samples, calculate test (statistics) value"] n5["* Use the GC to calculate the p-value"] end subgraph conclusion["(5) Conclusion"] n6{"Is the test value ..."} n7["'flucuating normally?'
p-value more than α
or test value not in critical region
"] n8["'too rare an occasion?'
p-value less than or equal to α
or test value within critical region"] n9["Reject H₀:
i.e surely obtaining the test value,
if it follows the test statistics under H₀ ,
is too rare an occasion that H₀ must be false."] n10["Do not reject null H₀;
i.e the test value flucuate quite 'normally',
all within the tolerence of the significant level,
so it is not a surprise its distribution is the test statistics under H₀"] end hypothesis --> significancelevel significancelevel --> statistics statistics --> calculations calculations --> conclusion n6 --> n7 & n8 n7 --> n10 n8 --> n9 n4 --> n5 n3 --> nd