Question

Describe an experiment that would require use of one of the three different t-tests (One Sample, Correlated Samples, or Independent Groups), but don’t tell us which statistic you think should be used. Then go into the discussion and look at another student's t-test experiment, and tell us which of the three t-test statistics would be appropriate to analyze his data.

Answer 1

Ans:

One Sample t - test:

Testing of significace :

   Null Hypothesis (H0): There is no significant difference between the population mean and sample

          10 individuals are chosen at random from a population and the heights are found to be in inches: 63, 63,66,67,68,69,70,70,71 and 71. Test whether the mean height in the population is 66 inches or not at 5% level of significance. For this problem we have to use one sample 't' test.

Independent Samples:

Testing of Significance:

          H0: There is no significant difference between two population means.

        For a random sample of 10 pigs fed on Diet A, the increase in weight in pounds in a certain period are 10, 6, 16, 17,13, 12, 14, 15, 9 Lbs. For another sample of 12 pigs fed on diet B, the increase in the same period were 7, 13, 22,15,12, 14,18,8,21,23,10,17 Lbs.

       Test whether diets A and B differ significantly as regards the effect on increase in wieght is concerned.

Correlated Samples:

Generally, two samples are independent, but in this case, the two sample are not independent and 1st sample size and 2nd sample size must be equal.

Ex: Memory capacity of 9 students was tested before and after training. Test at 5% level of significance whetehr the training was effective from the following scores:

Student:   1       2      3       4     5       6        7        8      9

Before:    10      15    9       3     7    12       16      17     4

After :      12      17   8        5     6      11       18      20     3

In this example, the samples (Students) are not independent when tested before and after training. In this case, For we have to use Paired t-test for test of significance.