Final MAT-274 Benchmark PDF

Preview

Summary

Download Final MAT-274 Benchmark PDF

Description

MAT 274 BENCHMARK FORMAT AND STYLE TEMPLATE 1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+# mg/dl and σ=#+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: a. Once? b. n=#+2 times, where # is the last digit of your student ID? c. n=#+4 times, where # is the last digit of your student ID? d. Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context. For each part, insert your sketch of the required area under the normal curve. In addition, include a screenshot of your Excel computation to find this area. i. Insert screenshot and figure for part (a)

ii. Insert screenshot and figure for part (b)

iii. Insert screenshot and figure for part (c)

iv. Comment on the relationship among the probabilities in parts (a),(b), and (c). I used the facts noted above to calculate the hazard of Rebecca being identified with gestational diabetes. I used the values given, the implied and preferred deviation, to measure the possibility. I have taken into consideration a connection between the graphs and the tables between widespread deviation and the central restrict theorem curve. because the curve or height began to increase, the standard deviation in each section commenced decreasing. I began with a standard deviation of 7 in part a. In the diagrams above, this relationship can be shown. It can also be found that the likelihood grows in size over this time. An instance of the way the opportunity may want to trade is as the sample length will increase, which can directly impact the central limit theorem curve as nicely. This is so extra periods will be monitored for blood glucose.

2. Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9# percent reliable, this means that the test will yield an accurate positive result in 9#% of the cases where the disease is actually present. Gestational diabetes affects #+1 percent of the population in our patient’s age group, and that our test has a false positive rate of #+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2: a. If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes? b. What is the probability of having the disease given that you test positive? c. If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes? d. What is the probability of having the disease given that you tested negative? e. Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted? Fill in the conditional probability table here, then answer the questions in each part below.

Part 2 diabetes No diabetes total

positive 6720 9300 16020

negative 280 83700 83980

total 7000 93000 100000

0.1 0.07 0.96

False positive affected reliable

Answer part (a) here.  The amount of people that will actually have gestational diabetes while testing positive would be 6,720 of the 100,000. Answer part (b) here. 

6,720/16,020 = 0.419 = 41.9% o The probability of you having gestational diabetes given that you test positive would be 41.9%.

Answer part (c) here.  280 of the 100,000 people will test negative, when they actually have gestational diabetes Answer part (d) here.  280/83,980 = .00333 = .33% o This would indicate that the probability of having gestational diabetes when testing negative would be .33%. Comment on how prevalence of the disease affects your ability to trust the test. Discuss what factors would lead you to trust the blood test, or not trust the blood test. The table and the data presented above illustrate the diploma of specificity on the subject of determining the diagnosis of one without or with gestational diabetes. The precision rate was .96, which can also be interpreted as 96 percent. Due to the fact that the health of patients may be at stake, precision when diagnosing a patient can be highly critical. The prevalence fee or effectiveness need to be ninety-nine or ninety nine percent, as it reveals that there could be little mistakes in terms of a affected person's misdiagnosis. the prevalence fee or reliability turned into .96 or 96% in this case, leaving a four or 4 percent danger that a mistake is probably made whilst diagnosing gestational diabetes. If the prevalence rate grew, it may serve to make the findings more precise and boost the test's reliability. Owing to the fact that there would be little risk of a mistake being made during their diagnosis, the reliability of the test would affect the patients. I will also trust the blood test because the risk of a misdiagnosis is reasonably low, given all the details.

3. 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 the following: a. A detailed discussion of your experimental design. Detailed experimental design should include the type of experiment, how you chose your sample size, what data is being collected, and how you would collect that data.

When it came to assess the effectiveness of a patient's diagnosis using a blood test, I first began by evaluating the sample amount of data I would use for my experiment. I started off by using a randomizer I was generated by the randomizer with a standard deviation of 6. Then I measured my margin of errors, which turned into 3.3, and my degree of consider, which was ninety five or 95%. I obtained a pattern length of thirteen when you consider that I implemented the margin of error, the populace trendy deviation and the confidence level in the calculator to degree the recognized sigma sample length. I had to be sure that there was a reasonable portion of the sample size, that it should not be too high or too little. Since the sample size is so high, it may not be possible for the patient to screen for glucose by sticking their finger each time. The sample size may be very important. Collecting an excessive amount of data may cause discomfort to the patient, but it is also not very useful to the experiment. This is attributed to the fact that no additional data is required. If the sample length is just too small, now not enough details may be received to guarantee maximum precision and reliability. b. How is randomization used in your sampling or assignment strategy? Remember to discuss how you would randomize for sampling and assignment, what type of randomization are you using? Randomized data is particularly relevant in an experiment and may have an effect on reliability. I used a website for randomization that provided me with random numbers in my preferred set. I used a program called Randomizer.org, because if I were to choose numbers on my own, I could pick and choose numbers that were skewed because they were the result of my experiment. Randonizer.org specified that in my target set, there was an option of 13 numbers. In data sets, randomization is used to look for real reliability and consistency. In the end, this will benefit the patient and the issuer of health care.

c. The type of inferential test utilized in your experiment. Include type of test used, number of tails, and a justification for this choice. A T-test changed into the inferential assay used at some point of this experiment. via the use of the hypothesized significance, which also can be proven because the average blood glucose level

of 140, I was able to measure the inferential examination. similarly, to make the sigma unknown on this test, the T check turned into also used. it is necessary to locate the reliability of the check, because the assumed cost become one hundred forty, I desired to locate values extra than 140 in my records series. sufferers with a glucose degree of greater than 140 should have gestational diabetes. Due to these reasons, a proper customized T test is required in this experiment to assess whether or not the measurements are accurate.

d. A formal statement of the null and alternative hypothesis for your test. Make sure to include correct statistical notation for the formal null and alternative, do not just state this in words. H0 : μ = 140 (null) H 1 : μ > 140 (alternative)

e. A confidence interval for estimating the parameter in your test. State and discuss your chosen confidence level, why this is appropriate, and interpret the lower and upper limits.

I used my randomized data set with a sample size of 13 and a confidence level of.95 or 95 per cent in this segment. Then I had to measure the random data set's mean and standard deviation. Then I used the "T confidence intervals" calculator to evaluate the higher and lower limits. By including my mean and general deviation from the random statistics set and coming into n, which is the sum of facts we had, I was able to degree the higher and decrease limits. I was cautioned after entering the requested information that the top restrict is 141.096 and the lower restrict is 137.366. because the maximum information length is 141,096 and the smallest is 137,366, the top and decrease parameters are significant.

f. An interpretation of your p-value and confidence interval, including what they mean in the context of your experimental design. Answer each part below. State your significance level, interpret your p-value, and make a decision on the null. With the knowledge made available by the previous sections, I was able to collect the information I needed to assess the reliability. To evaluate the p-cost and the choice of whether to simply accept or deny the null fee, I used the T importance check. For both the p-price and the

judgment, it became essential to ensure that I checked out the proper tail information. My p-price became .0276, which became smaller than my .05 significance level, which meant that the null speculation had to be discarded. Since I dismissed the negative, which implies that there was significant proof to refute the null, in other words, you support the conclusion. The null hypothesis was that there was no diabetes in the randomized data collection. I used the level of trust to assess how sure I was in my experiment. In my experiment, the degree of trust was 95 to 95 percent. Generally, you like to get a confidence rating of around.99 to 99 percent in most tests, because there is less chance of an error. The efficacy and the accuracy of the assessments and the diagnosis of gestational diabetes will be impaired by possessing a lower trust level....