A ttest is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. It is particularly useful when comparing the means of two groups to assess if the observed differences are statistically significant. The ttest calculates a test statistic, often denoted as “t,” which is then used to calculate a pvalue.
Null hypothesis (H0) and alternative hypothesis (H1):

 Null Hypothesis (H0): There is no significant difference between the means of premolt and postmolt data.
 Alternative Hypothesis (H1): There is a significant difference between the means of premolt and postmolt data.
 Calculate the tstatistic: It is calculated using the formula t=Mean difference/standard error of the difference
 Calculate the degrees of freedom (df): The degrees of freedom for an independent twosample ttest is given by df=n1+n2−2
 We can use a tdistribution table or a statistical software package to find the pvalue associated with the calculated tstatistic and degrees of freedom. Alternatively, most statistical software packages provide builtin functions to directly calculate the pvalue.
 We should check the assumptions of normality and equal variance for the two groups. If the variances are not approximately equal, we may need to use a modified ttest.Compare the pvalue to the significance level:
 If ≤p≤α, reject the null hypothesis (H0), indicating that there is a significant difference between the means.
 If >p>α, fail to reject the null hypothesis, suggesting that there is no significant difference between the means.
For our Crab data,
Step 1: Define Null and Alternative Hypotheses
 Null Hypothesis (H0): This is the default assumption that there is no significant difference between the groups we are comparing. it means that there is no significant difference between premolt and postmolt crab data.
 Alternative Hypothesis (Ha): This is what we want to test. It suggests that there is a significant difference between the groups.
Step 2: Collect Data
we can collect data for premolt and postmolt crab sizes. These are two groups for comparison.
Step 3: Perform the ttest
The ttest is a statistical test that calculates the tstatistic, which is a measure of how much the means of two groups differ relative to the variation in the data.
Step 4: Calculate the pvalue
The pvalue is a crucial result of the ttest. It represents the probability of observing the data that we have (or more extreme data) under the assumption that the null hypothesis is true (i.e., there is no significant difference between the groups). A small pvalue indicates that the observed data is unlikely to have occurred by random chance alone.
Step 5: Interpret the pvalue
To make a decision, we need to compare the pvalue to a significance level (alpha), typically set at 0.05. There are two possible outcomes:
 If pvalue < alpha: reject the null hypothesis (H0). This means that the data provides strong evidence that there is a significant difference between premolt and postmolt crab sizes.
 If pvalue ≥ alpha: fail to reject the null hypothesis (H0). This means that the data does not provide enough evidence to conclude that there is a significant difference between the groups.
Step 6: Make a Conclusion
Based on the comparison of the pvalue and alpha, we can conclude that there is a significant difference between premolt and postmolt crab sizes.