Question

The kid samples his primary carpenter ants and receives the following 5 measurements:
5mm 8mm 7.3mm 6.8mm 9mm

After feeding their primary ant hive a special diet, the kid measures the same random sample of ants in the same order. Their measurements are:
6mm 8.1mm 7.5mm 6.8mm 9mm

1. We want to know if this new diet means anything, is statistically significant or if it is essentially. For the first step, for each ant, subtract the new score from the old score and record this value. Be sure to keep track of your positives and negatives. What are your 5 measurements?
2. The null hypothesis becomes that the new mean (of your new data set computed in 1) is 0. Find the p-value associated with this situation. Can we reject the null hypothesis? Explain, show work, describe your process, and site resources used.

Answer 1

New Score-Old Score: 1, 0.1, 0.2, 0, 0.

The 5 measurements are: 1 mm, 0.1 mm, 0.2 mm, 0mm, 0mm.

Let X=no. of positive differences

Here we use paired sample sign test and alternative hypothesis is one sided.

Under null hypothesis, X follows Binomial(3,1/2) (since there two zeros are occurred)