Known standard deviation

Expected difference between two populations' mean

or or enter summarized data (x, n, σ, S) below

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When entering raw data, the tool will run the Shapiro-Wilk normality test and calculate outliers, as part of the test calculation.

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Example1: A man of average hight is expected to be 10cm taller than a woman of average hight (d=10)

Example2: The average weight of an apple grown in field 1 is expected to be equal in weight to the average apple grown in field 2 (d=0)

Hypotheses

H_{0}: μ_{1} ≥ = ≤ μ_{2}+d

H_{1}: μ_{1} < ≠ > μ_{2}+d

Test statistic

Normal distribution

Normal distribution | |

σ - The standard deviations of both populations are known ( so either σ_{1},σ_{2}_{1}=σ_{2} or ϭ_{1}≠ϭ_{2 }) | |

Expected difference d between the populations's average is known |

x_{1}, x_{2} - Sample average of group1 and group2 | |

n_{1},n_{2} - Sample size of group1 and group2 |

The following R code should produce the same results:

Currently, there is no direct R function for the two-sample z test.

__Examples__

1. Two tailed test example:

A factory uses two identical machines to produce plastic plates. You would expect both machines to produce the same number of plates per minute.

Let μ1 = average number of plates produced by machine1 per minute.

Let μ2 = average number of plates produced by machine2 per minute.

We would expect μ1 to be equal to μ2. If one of the machines is slower than the other one, it should be serviced. In this case, we would like to know both if μ1 < μ2 or μ1 > μ2, since either machine could be slower.

2. Left tail example.

A farmer uses fertilizer #1 with good results.

A friend told him fertilizer #2 is better than fertilizer #1.

Let μ1 = average number of potatoes per square meter in gardens using fertilizer #1.

Let μ2 = average number of potatoes per square meter in gardens using fertilizer #2.

The farmer assumes that the fertilizer currently in use (fertilizer #1) is better than the suggested one.(or equal)

He is willing to change fertilizer only if the new one is better.