Anonymous
Feb 16
By examples, discuss about Estimanation and Test of Hypothesis in statistics?
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Feb 16
Estimation and hypothesis testing are two fundamental concepts in statistics. They are used to make inferences about population parameters based on sample data. Here are some examples to illustrate these concepts:
1. Estimation:
Suppose you want to estimate the average height of all students in a school. You randomly select a sample of 100 students and measure their heights. The sample mean height is 165 cm. To estimate the population mean height, you can use this sample mean as a point estimate. Additionally, you can construct a confidence interval to provide a range of plausible values for the population mean. For example, a 95% confidence interval might be (160 cm, 170 cm), indicating that you are 95% confident that the true population mean height falls within this interval.
2. Hypothesis Testing:
Imagine a pharmaceutical company develops a new drug claiming it reduces cholesterol levels. To test this hypothesis, a clinical trial is conducted. The null hypothesis (H0) is that the drug has no effect on cholesterol levels, while the alternative hypothesis (Ha) is that the drug does reduce cholesterol levels. A random sample of 200 patients is divided into two groups: one receiving the drug and the other receiving a placebo. After the trial, the mean cholesterol level in the drug group is found to be significantly lower than in the placebo group. By conducting a hypothesis test, you can determine if the observed difference is statistically significant, providing evidence to support the alternative hypothesis.
These examples demonstrate how estimation and hypothesis testing are used in statistics. Estimation allows us to make educated guesses about population parameters based on sample data, while hypothesis testing helps us evaluate competing claims and make decisions based on the evidence provided by the data.
1. Estimation:
Suppose you want to estimate the average height of all students in a school. You randomly select a sample of 100 students and measure their heights. The sample mean height is 165 cm. To estimate the population mean height, you can use this sample mean as a point estimate. Additionally, you can construct a confidence interval to provide a range of plausible values for the population mean. For example, a 95% confidence interval might be (160 cm, 170 cm), indicating that you are 95% confident that the true population mean height falls within this interval.
2. Hypothesis Testing:
Imagine a pharmaceutical company develops a new drug claiming it reduces cholesterol levels. To test this hypothesis, a clinical trial is conducted. The null hypothesis (H0) is that the drug has no effect on cholesterol levels, while the alternative hypothesis (Ha) is that the drug does reduce cholesterol levels. A random sample of 200 patients is divided into two groups: one receiving the drug and the other receiving a placebo. After the trial, the mean cholesterol level in the drug group is found to be significantly lower than in the placebo group. By conducting a hypothesis test, you can determine if the observed difference is statistically significant, providing evidence to support the alternative hypothesis.
These examples demonstrate how estimation and hypothesis testing are used in statistics. Estimation allows us to make educated guesses about population parameters based on sample data, while hypothesis testing helps us evaluate competing claims and make decisions based on the evidence provided by the data.
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