The

Standard errors are important because they reflect how much sampling fluctuation a statistic will show. The inferential statistics involved in the construction of confidence intervals and significance testing are based on standard errors.

The

where σ is the standard deviation of the original distribution and N is the sample size (the number of scores each mean is based upon).

Suppose that the mean grade of students in a class is 62%, with a standard deviation of 10%. A sample of 30 students is taken from the class. Calculate the standard error of the sample mean and interpret your results.

You are given that μ = 62, and σ =10. Since n = 30, the standard error of the sample mean is: σ

Note that if you took a sample size of 50, the standard error would then be: σ

The standard error would drop as the sample size increased, which agrees with the information above.

When sample standard deviation (s) is used as an estimate of σ (when it is unknown), the estimated standard error of the mean is s/N

Suppose that the mean grade of students in a class is unknown, but a sample of 30 students is taken from the class and the mean from the sample is found to be 60%, with a standard deviation of 9%. Calculate the standard error of the sample mean and interpret your results.

Now, μ and σ are unknown, but m is given as 60 and s is given as 9. Since n = 30, you can estimate the standard error of the sample mean as: 9/30

It is important to note that when you have σ, you must use it; when you don't, you use its sample equivalent, s.

achu: std error = f(s, n) |

jpducros: Standart error formula is independant from the shape of the distribution (standart or not)....important... |

polanki: If S is given to sample which is standard deviation of sample or standard error then why again we need to devide it by sqrt N to get sample error. |

munro: polanki: it's the lowercase s, nor the uppercase S. |

Raok: may I ask how to differentiate between sample size and number of sample, isn't in this case, N is sample not same size? |

fanDango: You can have a sample size of 30 students from a population of 1000 students and also have 100 samples of 30 students. 100 is the number of samples, 30 is the sample size. |

Rachelle3: its always standard deviation divided by sample (of n) I get that but when you know this then you always do it the power of 0.5? |

mcbreatz: Power 0f .5 is same as taking the square root which is specified in the formula. |