I'm taking stats online which is making it even more difficult for me and I have nowhere to begin when answering this question.
1. A pharmaceutical industry claimed that their new product will lower the cholesterol level by an average of 14.5. To verify the claim, a laboratory tested the drug to a randomly selected one sample of 150 individuals for certain period and found that the new drug can reduce the cholesterol level by the by 12.4 with a standard deviation of 3.5. Assuming that the distribution is normal, follow the five steps hypothesis testing and test the validity of the claim at 95%.level.
Don't know what you are referring to with "the five steps," but here is a method.
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To test the validity of the pharmaceutical company's claim about their new product, you can follow the five steps of hypothesis testing. Here's how you can do it:
Step 1: State the hypotheses
The first step is to state your null hypothesis (H0) and alternative hypothesis (Ha). In this case, the null hypothesis would be that the average reduction in cholesterol level is equal to 14.5 (H0: μ = 14.5). The alternative hypothesis would be that the average reduction is different from 14.5 (Ha: μ ≠ 14.5).
Step 2: Formulate an analysis plan
Next, formulate an analysis plan that outlines the significance level you want to use (95% confidence level). This significance level, denoted as α, will help you decide whether to reject or fail to reject the null hypothesis.
Step 3: Analyze sample data
Now, it's time to analyze the sample data that you have. From the given information, you know that the sample mean reduction in cholesterol level is 12.4, and the standard deviation is 3.5. Since you have a sample size of 150, you can assume that the sample mean follows a normal distribution.
Step 4: Interpret the results
Using the sample data, calculate the test statistic and corresponding p-value. You can use a t-test since the population standard deviation is unknown. The test statistic (t) will tell you how many standard errors your sample mean is away from the hypothesized value of 14.5. The p-value will indicate the probability of obtaining a sample mean as extreme as the one observed, assuming that the null hypothesis is true.
Step 5: Make a decision
Based on the p-value obtained in step 4, compare it to the significance level (α). If the p-value is less than α (0.05 for a 95% confidence level), then you reject the null hypothesis. If the p-value is greater than α, you fail to reject the null hypothesis.
By following these steps, you can test the validity of the claim made by the pharmaceutical company and determine whether the new drug has a significant impact on reducing cholesterol levels.