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- Sampling Distribution and Estimation
- Sampling Error
- Estimation and Confidence Interval
- Interval Estimate of Population Mean
- Formula for the Sampling Distribution
- Z Score
- Z Value for Proportions
- Null Hypothesis (H0)
- Alternative Hypothesis (Ha)
- Hypothesis Testing
- Summary of Hypothesis Testing
- Purpose of Hypothesis Testing
- Steps of Hypothesis Testing
- p-Value Approach
- Critical Value Approach
- Critical Region
- Test Statistic
- Type I and Type II Errors

- It solves the problem of how good is an estimate in a sampling distribution.

- The sample mean estimates the population mean.

- The sample standard deviation estimates the population standard deviation.

- A point estimator cannot be expected to provide the exact value of the population parameter.

- An interval estimate can be computed by adding and subtracting a margin of error to the point estimate.

- The two confidence intervals that are used extensively are 95% and 99%.

= Sample Mean.

= Confidence Coefficient.

= value providing an area of in the upper tail of the standard.

is the population standard deviation.

= Sample Size.

Where,

Confidence coefficient

The value providing an area of in the upper tail of a distribution with degrees of freedom

S = Sample Standard Deviation

Sample Mean.

Population Mean.

Population Standard Deviation.

Sample Size.

is the hypothesized value of population proportion in the null hypothesis,

p = sample proportion,

n = sample size,

= standard deviation of the sampling distribution.

- A sample is selected from the population.

- The treatment is administered to the sample.

- After treatment, the individuals in the sample are measured.

- If the individuals in the sample are noticeably different from the individuals in the original population, we have evidence that the treatment has an effect.

- p-Value Approach, or

- Critical Approach

- Reject if the p-value < a.

- Do not reject (accept) if the p-value > a.

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- If it is large enough to be in the critical region, we conclude that the difference is significant or that the treatment has a significant effect.

- In this case we “reject the null hypothesis”.

- If the mean difference is relatively small, then the test statistic will have a low value.

- In this case, we conclude that the evidence from the sample is not sufficient, and the decision is “fail to reject the null hypothesis”.

Population Condition |
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Conclusion | True | False |

Accept (Conclude | Correct Decision | Type II Error |

Reject (Conclude | Type I Error | Correct Decision |

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