A medical researcher gave 100 patients a new drug to see if it reduces their blood pressure? Did the new drug reduce the patients' blood pressure? Write your hypothesis mathematically.

Not sure how to do this, Prob & Stats has been quite a struggle for me

To write the hypothesis mathematically, we can use the following notation:

H0: μ = μ0
The null hypothesis (H0) states that the mean blood pressure (μ) of the patients is equal to a specified value (μ0), meaning the new drug has no effect in reducing blood pressure.

H1: μ < μ0
The alternative hypothesis (H1) suggests that the mean blood pressure (μ) of the patients is less than the specified value (μ0), indicating that the new drug does reduce blood pressure.

Using this notation, the hypothesis can be written as:
H0: μ = μ0
H1: μ < μ0

Where:
μ represents the population mean blood pressure after administration of the new drug.
μ0 represents the specified value of the population mean blood pressure that we want to test against.

To determine if the new drug reduces the patients' blood pressure, statistical analysis should be conducted on the data collected from the 100 patients.

To determine whether the new drug reduces the patients' blood pressure, we can formulate a hypothesis mathematically. In statistics, we typically use the null hypothesis (H0) and the alternative hypothesis (Ha).

The null hypothesis (H0) states that there is no effect or relationship between the new drug and the patients' blood pressure. Assuming that the drug has no effect, we can express the null hypothesis as:

H0: The mean blood pressure of the patients who received the new drug is equal to the mean blood pressure of the general population.

On the other hand, the alternative hypothesis (Ha) states that there is a significant effect of the new drug on reducing the patients' blood pressure. We can express the alternative hypothesis as:

Ha: The mean blood pressure of the patients who received the new drug is significantly lower than the mean blood pressure of the general population.

To determine whether the new drug reduced the patients' blood pressure, we would need data to compare the mean blood pressure of the patients before and after receiving the drug, or compare it with a control group.

Given that you mentioned a medical researcher gave the drug to 100 patients, it suggests that you might have the necessary data. In order to test the hypothesis, you would need to calculate the mean blood pressure and determine if it is significantly lower than the mean blood pressure of the general population, using appropriate statistical tests such as a t-test or analysis of variance (ANOVA).

It is important to note that this explanation serves as a general guideline, and further steps would be required to actually test the hypothesis using the available data. Consulting with a statistician or seeking guidance from your instructor could be very helpful in understanding and implementing the appropriate statistical tests.