Question

• Write a report about hypothesis test ans confidenr interval the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.

Answer 1

Test of Significance (Hypothesis testing)

• In the process of analysis, relationships or differences supporting or conflicting with the original or new hypotheses should be subjected to tests of significance to determine with what validity data can be said to indicate any conclusion.
• The study of test of significance which enable us to decide on the basis of sample if the deviation between the observed and parametric value
• Two independent sample statistics is significant or might be attributed to the fluctuation of sampling.
• Statement concerning an observed random variable X is called statistical hypothesis. E.g.

1. X is a random variable
2. X is a continuous random variable
3. X is a binomial variate with parameter p=1/2
4. X is a binomial variate with parameter p<1/2
5. X is a Poisson variate with paramet λ =2
6. X is a normal variate with mean µ= 2 and σ = ?

Statistical Hypothesis classified into two

(A) Non parametric Hypothesis

(B) Parametric Hypothesis

(A) Non parametric Hypothesis- A statistical hypothesis which does not say anything about parameter of the population distribution under the consideration.

1. X is a random variable
2. X is a continuous random variable

(B) Parametric Hypothesis- A statistical hypothesis which describe the parameter or parameters of the population.

1. X is a binomial variate with parameter p=1/2
2. X is a binomial variate with parameter p<1/2
3. X is a Poisson variate with parameter λ =2
4. X is a normal variate with mean µ= 2 and σ =?

A parametric Hypothesis further classified into two

• Simple Hypothesis- A parametric hypothesis which describes all parameters of distribution or population.

1. X is a binomial variate with parameter p=1/2
2. X is a Poisson variate with parameter λ =2

• Composite Hypothesis-A parametric Hypothesis may describe a few parameter uniquely or even non of the parameters uniquely is called composite hypothesis.

1. X is a binomial variate with parameter p<1/2

• Analyze sample data. Find the value of the test statistic (mean score, proportion, t statistic, z-score, etc.) described in the analysis plan.
• Interpret results. Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null hypothesis, reject the null hypothesis.

Confidence Interval-A 95% confidence interval is a different kind of estimate. It consists of two numbers L (lower) and U (upper), which are derived from the sample in some way without knowledge of the unknown parameter P. Confidence interval to express the degree of uncertainty associated with sample statistic.A confidence interval is an estimate combined with a probability.

e.g. Let us assume that we conducted a survey and computed interval estimate based on survey data.We use Confidence Interval to describe uncertainty associated with Interval estimate. We describe the interval estimate as a 95% Confidence Interval. This means that if we used the same sampling method to select different samples and computed an interval estimate for each sample, we would expect true population parameter to fall within the interval estimates 95% of that time.

Confidence Interval - Confidence Interval Indicates

• The precision of the estimate.
• The uncertainty of the estimate.