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Statistics : Confidence Interval Tutorials

Confidence interval for means t equal variances

  • STATISTICS
Confidence interval for difference in means when variances are unknown and equal Let $x_1, x_2, \cdots, x_{n_1}$ be a random sample of size $n_1$ from a population with mean $\mu_1$ and standard deviation $\sigma_1$. Let $y_1, y_2, \cdots, y_{n_2}$ be a random sample of size $n_2$ from a population with mean $\mu_2$ and standard deviation $\sigma_2$. And the two sample are independent. Let $\overline{x} = \frac{1}{n_1}\sum x_i$ and $\overline{y} = \frac{1}{n_2}\sum y_i$ be the sample means of first and second sample respectively.
2 min Read 1

Confidence Interval for Mean

  • STATISTICS
Introduction Confidence interval can be used to estimate the population parameter with the help of an interval with some degree of confidence. One such a parameter that can be estimated is a population mean. In this article we will discuss step by step procedure to construct a confidence interval for population mean when the population standard deviation is known. Confidence Interval for Mean Let $X_1, X_2, \cdots , X_{n}$ be a random sample of size $n$ from $N(\mu, \sigma^2)$ with known variance $\sigma^2$.
2 min Read 1

Confidence Interval for Mean examples

  • STATISTICS
Confidence Interval for Mean In this tutorial we will discuss some numerical examples to understand how to construct a confidence interval for population mean when the population standard deviation is known. Example 1 Among those who take the Graduate Record Examination (GRE), 67 persons are randomly selected. This sample group has a mean score of 558 on the quantitative portion of the GRE. The population standard deviation is 139 (from the Educational Testing Service).
3 min Read 2

Confidence Interval for Mean-t

  • STATISTICS
Introduction Confidence interval can be used to estimate the population parameter with the help of an interval with some degree of confidence. One such a parameter that can be estimated is a population mean. In this article we will discuss step by step procedure to construct a confidence interval for population mean when the population standard deviation is unknown. Confidence Interval for the mean ($\sigma$ unknown) Let $X_1, X_2, \cdots , X_{n}$ be a random sample of size $n$ from $N(\mu, \sigma^2)$ with unknown variance $\sigma^2$.
2 min Read 1

Confidence Interval for mean-t examples

  • STATISTICS
Confidence Interval for the population mean when standard deviation is unknown This tutorial covers examples on confidence interval for the population mean when the population standard deviation is unknown. Example 1 A new brand of laptop battery is produced by a company. The company claims that the battery will last for an extended period of time before a recharge is necessary. A sample of 40 batteries is tested for the length of usage time to recharge.
4 min Read 3

Confidence Interval for Means

  • STATISTICS
Introduction In this article we will discuss step by step procedure to construct a confidence interval for difference between two population means when the population standard deviations are known. CI for difference between two population means (variances are known) Let $X_1, X_2, \cdots, X_{n_1}$ be a random sample of size $n_1$ from a population with mean $\mu_1$ and standard deviation $\sigma_1$. Let $Y_1, Y_2, \cdots, Y_{n_2}$ be a random sample of size $n_2$ from a population with mean $\mu_2$ and standard deviation $\sigma_2$.
2 min Read 1

Confidence Interval for Means Examples

  • STATISTICS
CI for difference between two population means (variances are known) In this tutorial we will discuss some examples on confidence interval for difference in means when the population variances are known. Example 1 Two kinds of thread are being compared for tensile strength. Fourty pieces of each type of thread are tested under similar conditions. Brand A has an average tensile strength of 81.6 kilograms with a standard deviation of 4.
4 min Read 2

Confidence interval for means t equal variances examples

  • STATISTICS
Confidence interval for difference in means when variances are unknown and equal In this tutorial we will discuss step by step solution to some numerical problems on confidence interval for difference in means when the population variances are unknown and equal. Example 1 A high school language course is given in two sections, each using a different teaching method. The first section has $21$ students, and the grades in that section have a mean of $82.
4 min Read 3

Confidence Interval for Paired t

  • STATISTICS
Confidence Interval for paired t-test Let $X_1, X_2, \cdots, X_n$ and $Y_1, Y_2, \cdots, Y_n$ be two dependent samples each of size $n$ with respective means $\mu_1$ and $\mu_2$. Define $d_i = X_i - Y_i$, $i=1,2,\cdots, n$. Let $\overline{d}=\frac{1}{n} \sum d_i$ be the mean of the difference and $s_d=\sqrt{\frac{1}{n-1}\sum (d_i - \overline{d})^2}$ be the sample standard deviation of the difference. Let $C=1-\alpha$ be the confidence coefficient. Our aim is to construct $100(1-\alpha)$% confidence interval estimate of the mean of the differences from dependent samples.
2 min Read 1

Confidence Interval for Paired t examples

  • STATISTICS
Confidence Interval for paired t-test In this tutorial we will discuss how to determine confidence interval for the difference in means for dependent samples. Example 1 An experiment ws designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair.
6 min Read 4

Confidence Interval for Proportion

  • STATISTICS
Introduction Confidence interval can be used to estimate the population parameter with the help of an interval with some degree of confidence. One such a parameter that can be estimated is a population proportion. In this article we will discuss step by step procedure to construct a confidence interval for population proportion. Confidence Interval for Proportion Let $X$ be the observed number of individuals possessing certain attributes (number of successes) in a random sample of size $n$ from a large population with population proportion $p$.
2 min Read 1

Confidence Interval for Proportion examples

  • STATISTICS
Confidence Interval for Proportion In this tutorial we will discuss some numerical examples to understand how to construct a confidence interval for population proportion. Example 1 In a simple random sample of 50 animated children movies, 19 show tobacco use by main characters. Construct a 90% confidence interval to estimate the proportion of all animated children movies that show tobacco use by main characters. Assume the population is normally distributed.
4 min Read 2