Statistical Inference – Point – Interval Estimation.

- statistical inference
- estimation
- point estimation
- interval estimation

The act of drawing generalization on a population parameter based on sample statistics. the statistical data used to draw conclusion, it is drawn with certain degree of certainty. casual inference deals with drawining conclusion based on cause of a particular thing.

statistical inference that deals with drawing conclusion is based on empirical data which is divided into

- estimation
- Null hypothesis test

Estimation id s process of using a range of values to estimate or approximate a population parameter using sample statistics or data. the test and estimate both make use of sample data in order to drawing conclusion.

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the null hypothesis test find out if a difference exist between two or more variables and estimation tries to determine the proportion or magnitude of the difference maximum likelihood for parameter.

point estimation refers to using a single value to approximate or estimate or explain a population parameter using sample statistics.

interval estimation involves using range of values in order to explain the population parameter from a given sample. when the interval estimation is met with a degree of certainty or probability level, it is called confidence interval.

Correlation Coefficient for One – Two Samples In Hypothesis Testing

**Estimating with neu and X-bar**

sampling distribution of mean is a hypothetical distribution that tries to describe the means of sample for a given distribution. for example assuming a distribution is normally distributed with the following parameters

X-bar = 3.42, n = 16, SD = 0.68, 99% C.I = 1% = 0.01 = 2.58 from the standard z- table. this is accomplished by going to the z – table, search for 0.01 under two – tailed table and tracing the z- value.

C.I = X-bar +/- z xSD/Sqr(n)

= 3.42 +/- 2.58 x 0.68 / sqr(16)

= 3.42 +/- 0.44

= 3.42 – 0.44, 3.42 + 0.44

= (2.98, 3.86)

Sampling error and normal distribution

**Example 2**

The mean and standard deviation for the quality grade point average a random sample of 49 students are calculted to be 2.2 and 0.3 respectively. find the 95% confidence interval for the population mean.

solution

given the following parameters

n = 49, X-bar = 2.2, SD = 0.3, Aplha level = 0.05 = 1.96

C.I = X-bar +/- z xSD/Sqr(n)

= 2.2 +/- 1.96 x 0.3/sqr(49)

= 2.2 – 0.082 , 2.2 + 0.082

= (2.118, 2.282)

**Assignment**

in a random sample of 1000 voters, 580 were for candidate A, while 420 were for candidate B. construct a 95% confidence interval for the population of voters for candidate A.

Statistical Inference – Point – Interval Estimation.

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