Question

1. a researcher suggests that small doses of hyaluronic acid (ha) will promote the uptake of water in human skin, thus reducing symptoms of dryness and dehydration. he suggests that ha binds to water and prevents it from evaporating off of the skin. the researcher creates a skin cream formulated with ha and compares the skin of 100 people before and after use of the cream. formulate one null (h₀) and one alternative (h₁) hypothesis. describe the data you would expect to see that would support the null hypothesis.

Explanation:

Null Hypothesis (\(H_0\)):

The null hypothesis states that there is no effect or no difference. In this context, it would be that small doses of hyaluronic acid (HA) do not promote water uptake in human skin, and thus do not reduce symptoms of dryness and dehydration. Mathematically, we can frame it as: There is no significant difference in the skin's water uptake (or measures of dryness/dehydration) before and after the use of the HA - formulated skin cream.

Alternative Hypothesis (\(H_1\)):

The alternative hypothesis is what the researcher is suggesting. So, small doses of hyaluronic acid (HA) do promote water uptake in human skin, and this leads to a reduction in symptoms of dryness and dehydration. In other words, there is a significant difference in the skin's water uptake (or measures of dryness/dehydration) before and after the use of the HA - formulated skin cream, with the after - use measures showing improved water retention (less dryness/dehydration).

Data for Null Hypothesis Support:

To support the null hypothesis, we would expect to see that when we measure the relevant variables (such as skin moisture levels, measures of dryness like flakiness scores, or dehydration - related skin characteristics) in the 100 people, there is no significant difference between the measurements taken before using the HA - formulated cream and the measurements taken after using the cream. For example, if we use a scale from 1 - 10 to measure skin dryness (where 1 is very dry and 10 is very moist), the average dryness score before using the cream and the average dryness score after using the cream would be approximately the same (within the margin of error of the measurement). Or, if we measure skin water content using a suitable instrument, the water content before and after cream application would not show a statistically significant increase.

Answer:

• Null Hypothesis (\(H_0\)): Small doses of hyaluronic acid (HA) do not promote water uptake in human skin and do not reduce symptoms of dryness and dehydration (i.e., there is no significant difference in skin water uptake/dryness - related symptoms before and after using the HA - formulated skin cream).
• Alternative Hypothesis (\(H_1\)): Small doses of hyaluronic acid (HA) do promote water uptake in human skin and reduce symptoms of dryness and dehydration (i.e., there is a significant difference in skin water uptake/dryness - related symptoms before and after using the HA - formulated skin cream, with post - use showing improved water retention/less dryness).
• Data for \(H_0\) Support: When measuring skin moisture, dryness (e.g., flakiness, dryness scores), or dehydration - related characteristics in the 100 people, there is no significant difference between pre - cream and post - cream application measurements (e.g., average dryness scores or skin water content are approximately the same before and after cream use).