One and Two Sample Test of Hypothesis

Statistical Decision: - Very often is practice; we are called upon to make decisions about population on the basic of sample information; such decisions are called Statistical Decision.

Statistical Hypothesis: - Such assumptions about the population may or may not be true are called Statistical Hypothesis.

Null Hypothesis: - If we want to decide whether one assumption or procedure is letter than another. Null Hypothesis is the positive rejection of Hypothesis. It is defined as Ho.

Alternative Hypothesis: - The Alternative Hypothesis is the logical opposite to the Null Hypothesis. It is defined as Ha.

One Tail Test: - A test of any Statistical Hypothesis where the alternative is one sided such as

Ho : μ = μ_o or Ho : μ = μ_o

Ha : μ > μ_o or Ha : μ < μ_o

Is called one Sided Test.

Two Tailed Test: A test of any Statistical Hypothesis where the alternative is two sided such as

Ho : μ = μ_o

Ha : μ ≠ μ_o

Is called Two Sided Test.

A test of the mean of a normal distribution against two sided alternative:

A test of the mean of a normal distribution against right sided alternative:

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Graphical Distribution of Frequency Distribution

Frequency distribution can be presented graphically in any one of the following ways: Histogram Frequency Polygon Smooth Frequency Curve Cumulative Frequency Curve of Ogive Curve Pie-Chart Histogram: - A histogram is an area diagram in which the frequencies corresponding to each class interval of frequency distribution are by the area of a rectangle without leaving no gap between the cosective rectangles. Frequency Polygon: - This is one kind of histogram which is represented by joining the straight lines of the mid points of the upper horizontal side of each rectangle with adjacent rectangles. Smooth Frequency Curve: - This is one kind of histogram which is represented by joining the mid points by free hand of the upper horizontal side of each rectangle with adjacent rectangles. Comulative Frequency Curve or Ogive Curve: - The total frequency of all values less then the upper class boundary of a...

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Statistics & Probability

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