Dont need the problems solved just a thorough explanation as to why that test would be used for that scenario

For this practice activity, read the scenario below and determine which type of test is better, a 2 sample t test or a 1 sample matched pairs t test. Explain your reasoning. Respond to two of your classmates on whether you agree or disagree with what they chose. 1. A researcher wants to prove that counter height in relation to a person's elbow height affects the amount of time it takes to complete a kitchen task. Mo re specically, the higher the counter is in relation to the person's elbows, the ionger it would take to complete a task. A 5% level of signicance is used to exam whether or not it takes 10 women of equal height and eibow distance longer to peel a potato with the nonstanda rd 44foot counter height than with a standard 13foot counter height. The average time it took the women to peel the potato at the 11-foot counter was 10 seconds while it only took them 5 seconds at the 11-foot counter. The standard deviation of the difference was 2.9 seconds and the standard error was 2.498. Assume an normal distribution. 2. A new facial cleansing system is developed by the New You Beauty Corporation. They claim that the people who use their system regulariy and for the same amount of time have the same results as those who use the cleansing system reguiarly that is manufactured by Hidden Youth Beauty Corporation. A random sample of 12 women who use the New You system show an improvement ranked at 20 with a standard deviation of 4. Of the 10 sampled who use the Hidden Youth system show an improvement ranked at 22 with a standard deviation of 3. Researchers are trying to determine whether the results provided are sufcient evidence to support the claim by New You assuming the population variances are not equal