Hypothesis Testing - Framework
Hypothesis?testing is a form of?statistical inference?that uses data from a sample to draw conclusions.
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5 steps of Hypothesis Testing:
?? Step-1 : Setup hypothesis and determine level of significance
?? Setup Null hypothesis (H0) from population parameters
?? Setup Alternative hypothesis (H1)
?? Setup appropriate significance level,α
?? Step-2 : Compute test statistic
?? From H1, determine whether this is an upper, lower, or two-tailed test
?? Depending on sample size select appropriate sample distribution (t-statistic or Z-statistic
?? Compute test statistic?
?? Step-3 : Determine critical value(Zα) of test based on a ( level of significance)
?? Step-4 : Compare Z with Zα, and conclude test
?? Step-5 : Decision Rule
?? if I Z l< Zα, Z is not significant and null hypothesis may therefore be accepted
?? if I Z I≥ Zα, Z is significant and null hypothesis is rejected
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Will share more later, follow? Mukesh Manral???? ?for more details.
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?? Understanding Hypothesis Testing with an example:
?? Chips company claims that maximum saturated fat content in chips packet is 2 grams with (std dev = 0.25)
A test on a sample of 35 packets reveal that mean saturated fat is 2.1 grams
?? Should claim of Chips company be rejected?
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?? Let’s test the null hypothesis at the significance level of 5%
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?? Step 1:?Set up null hypothesis and alternative hypothesis
H0 : mu <= 2
Null Hypothesis
H1 : mu > 2
Alternative Hypothesis – Upper tailed test
level of significance = 0.05
?? Step 2: Compute?Test Statistics
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Sample size id more than 30. So, need to calculate Z statistics mu = 2
Population mean Xbar = 2.1
Sample mean sigma = 0.25
Population Std Dev n = 35
Sample Size SE = sigma/sqrt(n)
Sample std deviation: 0.0422 Z = (Xbar – mu)/SE
Z score – Z??– 2.36 std dev away from the mean
?? Step 3: Compute?critical value for significance level?= 0.05 or Confidence Interval = 95%
Zα = qnorm(1-α)
Zα – Critical value for 95% confidence
?? Step 4:?Compare?Test statistic with critical value?and conclude the test
Decision
if Z < Zα, Z is not significant and the null hypothesis may, therefore, be accepted.
if Z ≥ Zα, Z is significant and the null hypothesis is rejected Z > Zα
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?? Conclusion:
With 95% confidence claim of at most 2 grams of saturated fat in a chips packet should be rejected
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?? Chances of Error in Sampling:
?? TYPE I Error:
When we reject the null Hypothesis, although that Hypothesis was true, it is called as TYPE I Error. This type of error is denoted by alpha(α).
In Hypothesis Testing, the normal curve that shows the critical region is called the alpha region
?? TYPE II error:
When we accept the null Hypothesis but it is false then it is called as TYPE II error. This type of error is denoted by (β).
In Hypothesis Testing, the normal curve that shows the acceptance region is called the beta region
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Will share more later, follow Mukesh Manral???? ?for more details.
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