Question

As we have seen in class, hypothesis testing and confidence intervals are the most common inferential tools used in statistics. Imagine that you have been tasked with designing an experiment to determine reliably if a patient should be diagnosed with diabetes based on their blood test results. Create a short outline of your experiment, including all of the following:

1. A detailed discussion of your experimental design.
2. How is randomization used in your sampling or assignment strategy?
3. The type of inferential test utilized in your experiment.
4. A formal statement of the null and alternative hypothesis for your test.
5. A confidence interval for estimating the parameter in your test.
6. An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design

Answer 1

Solution :

As we have seen in class, hypothesis testing and confidence intervals are the most common inferential tools used in statistics. Imagine that you have been tasked with designing an experiment to determine reliably if a patient should be diagnosed with diabetes based on their blood test results.

We have to determine if a patient should be diagnosed with diabetes based on blood test results.

For this we need a sample size of >=30

We need to check if blood test results accurately predict the diabetes.

Null hypothesis: H0: blood test results doesn't accurately predict the diabetes.

Alternate hypothesis: HA : blood test results accurately predict the diabetes.

Let's assume 95% confidence interval which means 95% chances that blood test results accurately predict the diabetes.

In our research we take 30 diabetic patients and take their blood test. For 95% CI the blood test should correctly diagnose atleast 95% of patients = 95% of 30 = 28.5 ~ 29. Hence if blood test results diagnose 29 or more patients as diabetic then we reject null hypothesis.

95% confidence interval means p value of 0.05

Lower the p value more accurate is our research. A p value of 0.01 would mean that 99% chance that blood test results accurately predict the diabetes.

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