In the realm of statistics and data analysis, the graph t distribution reigns supreme as a versatile tool that empowers businesses with deeper insights and more accurate predictions. This distribution, also known as the Student's t distribution, is a continuous probability distribution that estimates the population mean when the sample size is small and the population standard deviation is unknown.
Property | Description |
---|---|
Symmetric | The graph t distribution is symmetric around the mean. |
Bell-Shaped | It has a bell-shaped curve, similar to the normal distribution. |
Flatter Tails | The tails of the graph t distribution are flatter than the normal distribution, indicating that extreme values are more likely to occur. |
Degrees of Freedom | The shape of the graph t distribution is determined by the degrees of freedom, which represent the sample size minus one. |
1. Hypothesis Testing
Hypothesis | Test Statistic | P-Value | Conclusion |
---|---|---|---|
H0: μ = 100 | t = (105 - 100) / (5 / √10) = 2.24 | 0.04 | Reject H0 |
H1: μ ≠ 100 |
Note: A P-value less than 0.05 indicates statistical significance at the 5% level.
2. Confidence Interval Estimation
Confidence Level | t-Value | Confidence Interval |
---|---|---|
90% | 1.645 | (95, 105) |
95% | 1.960 | (90, 110) |
99% | 2.576 | (85, 115) |
3. Significance Testing for Proportions
The graph t distribution is an essential tool for businesses seeking to unlock actionable insights from data. By leveraging its unique properties, businesses can improve hypothesis testing, establish confidence intervals, and assess proportions accurately. With its versatility and wide-ranging applications, the graph t distribution empowers businesses to make informed decisions, enhance efficiency, and maximize success.
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