Probability Test

The assumption for a single sample t test can be listed as follows:

1. The sample used should be random.
2. The random sample should be taken from independent observations.
3. The population distribution must be nearly normal or the size of sample should be large.

The purpose of this test is to state wherever there is significant difference between the hypothesized mean and the observed sample mean. If the difference is large the hypothesized population mean is rejected. If the difference is small we fail to reject the hypothesized population mean.

The inputs to the test can be summarized as follows:

• Sample population= 1,2,3,4,5,6
• The null Hypotheses (Ho)=0
• The alternative Hypotheses (Ha)≠0
• The level of Significance =0.05
• Sample size (n) = 6

From this inputs the console also calculates the sample mean(x̅ )= 3.5, the standard deviation (σ)

which is 1.870828693387. It can aslo be determined that the critical values are tcrit= ± 2.571 when relating to the T table for a 0.05 level of Significance and a degree of freedom (n-1) of 5.

T values, t = 4.5826, is a standardized value which represents the difference between the samplle mean and the hypothesized mean. It is calculated by the difference between the sample mean and the hypothesized mean divided by the standard error (standard error =standard deviation divide by square root of sample size).  As shown below.

[pic 1]

Hence [pic 2]

The next element of the output df is the degree of freedom. It represents the number of values in the calculation that can vary without affecting the sample mean. It is calculated using 1-n which in this case is 5.

Then we have the p value which represents the probability that the null hypothesis is true. The large the p-value the higher the probability that the hypothesized sample mean (0 in this example) is true.

The alternative Hypotheses represent the outcome if the null hypothesis is rejected. In this case the alternative hypothesis is Ha ≠0. margin of error