Case study #1 – A p value of 0.96 means there is a very high probability that the null hypothesis is true. The evidence suggests no significant difference between means and that the drug is ineffective.
Case study #2 – With p < 0.001 the difference is highly significant. Evidently your drug has the opposite effect in people than it did in rats. You have strong evidence that it causes weight gain.
Case study #3 – You cannot reject the null hypothesis that the hormone does not extend the life of your cultures. This conclusion does not mean that the result itself is insignificant, though. For many studies the result is no significant difference between means. That finding can be significant in terms of the science. We use the phrase "significant difference" to refer to a comparison between means. Significance in the other sense refers to the importance of the finding, regardless of outcome.
Case study #4 –A p value of 0.07 does not reach the arbitrary 0.05 cutoff for a marginally significant difference. However, you came so close that a single data point might have made the difference. If the stakes are high then it might be worth repeating the experiment. You might look for sources of random error that you can eliminate or minimize, and maybe expand the number of replicate samples. Of course if you again cannot reject the null hypothesis then the chances are whatever effect your treatment has, it may not be not large enough and/or consistent enough to warrant further experiments.
DONE!