Null hypothesis (H0): The mean sorbic acid residual concentrations before and after storage in ham are equal.
Alternative hypothesis (H1): There is a significant difference in mean sorbic acid residual concentrations before and after storage in ham.
The paired samples t-test is a statistical method used to determine if there is a significant difference between the means of two related groups.
In this case, the null hypothesis (H0) and alternative hypothesis (H1) can be set up as follows:
Null Hypothesis (H0): There is no effect on the mean sorbic acid residual concentrations after storage.
Alternative Hypothesis (H1): There is a significant effect on the mean sorbic acid residual concentrations after storage.
Mathematically, this can be expressed as:
H0: μ_before = μ_after
H1: μ_before ≠ μ_after
where μ_before is the population mean sorbic acid residual concentration before storage, and μ_after is the population mean sorbic acid residual concentration after 60 days of storage.
The paired samples t-test will assess whether the observed differences between the paired samples (before and after storage) are statistically significant.
The test will consider the means of the two groups and the variability within each group.
Using a 2-tailed test at a 0.01 significance level means that you are looking for extreme values in both tails of the distribution, and you want the p-value to be less than 0.01 to reject the null hypothesis.
After conducting the paired samples t-test on the provided data, if the p-value is less than 0.01, you would reject the null hypothesis and conclude that there is a significant effect on the mean sorbic acid residual concentrations after storage.
If the p-value is greater than 0.01, you would fail to reject the null hypothesis, suggesting no significant effect.