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MAT 255 Grand Canyon University Probability and Inferential Statistics Questions
Assessment Description1. A patient is classified as having gestational diabetes if their glucose level is above 140 millig ...
MAT 255 Grand Canyon University Probability and Inferential Statistics Questions
Assessment Description1. A patient is classified as having gestational diabetes if their 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+X mg/dl and σ = X+1 mg/dl, where X is the last digit of your GCU student ID number. What is the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:Once?X+1 times, where X is the last digit of your student ID?X+4 times, where X is the last digit of your student ID?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.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 9X percent reliable, gestational diabetes affects X+1 percent of the population in our patient’s age group, and that our test has a false positive rate of X+4 percent. Compute the following quantities based on this new information:If 100,000 people take the blood test, how many people that test positive will actually have gestational diabetes?What is the probability of having the disease given that you test positive?If 100,000 people take the blood test, how many people that test negative despite actually having gestational diabetes?What is the probability of having the disease given that you tested negative?Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?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 of the following:A detailed discussion of your experimental design.How is randomization used in your sampling or assignment strategy?The type of inferential test utilized in your experiment.A formal statement of the null and alternative hypothesis for your test.A confidence interval for estimating the parameter in your test.An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design
5 pages
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Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: The annual income levels and annual expend ...
Solution
Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: The annual income levels and annual expenditure on food and fruits are ...
Cuyamaca Alcoholic Drinks Consumed by Students at A Liberal Arts College HW
PromptIn a previous lab we tested the following hypotheses, H 0: μ = 4.73 and H a: μ < 4.73 (where μ is the mean num ...
Cuyamaca Alcoholic Drinks Consumed by Students at A Liberal Arts College HW
PromptIn a previous lab we tested the following hypotheses, H 0: μ = 4.73 and H a: μ < 4.73 (where μ is the mean number of alcoholic drinks consumed by students at a liberal arts college).In a random sample of 75 students, the mean was 3.93 alcoholic drinks consumed in a week. Here is the StatCrunch output from the hypothesis test.μ: Mean of variableH 0: μ = 4.73H A: μ ≠ 4.73Hypothesis test resultsVariableSample MeanStd. Err.DFT-StatP-valuenumber of drinks per week3.9333333 0.43592434 74 -1.8275343 0.0717 Using this context and the StatCrunch output, explain the meaning of each of the following.
Std. Err (standard error)T-stat (T-score)P-valueIn a previous matched pairs lab we tested the following hypotheses, where μ is the mean of the differences in corn yield for a plot of land (regular seed minus kiln-dried): H0: µ = 0 and Ha: µ < 0. In a random sample of 11 seeds of each type, the mean of the differences in the sample was -33.7. Here is a StatCrunch print-out of the hypothesis test.Paired T hypothesis test:μ D = μ 1 − μ 2: Mean of the difference between Regular seed and Kiln-dried seedH 0: μ D = 0H A: μ D < 0
Hypothesis test resultsDifferenceMeanStd. Err.DFT-StatP-valueRegular seed - Kiln-dried seed-33.72727319.95134610-1.69047610.0609Differences stored in column, Differences.Using this context and the StatCrunch output, explain the meaning of each of the following.
Std. Err (standard error)T-stat (T-score)P-value.
Conditional probabilities
Finding a conditional Probability:
Example
Let's look at a standard deck of 52 cards.
What is the probability of getting 2 ...
Conditional probabilities
Finding a conditional Probability:
Example
Let's look at a standard deck of 52 cards.
What is the probability of getting 2 kings assuming that the first one is not replaced?
4/52 * 3/51 = 1/13*1/17= 1/221
What is the probability of getting 2 kings assuming that the first one is replaced?
4/52 * 4/52 = 1/13 * 1/13 = 1/169
Instructions
Now for your main post do a similar problem using with replacement and without replacement. You can use a card problem as long as it is not 2 kings.
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Most Popular Content
5 pages
Regional Real Estate Company
Are The regional average market price of places of residence in my area higher than the Population Parameter: Average (Mea ...
Regional Real Estate Company
Are The regional average market price of places of residence in my area higher than the Population Parameter: Average (Mean) of the national places of ...
The Szabo vs Reliable Car Parts Corporation fuel pumps Legal Memorandum
Write a Memorandum.Appendix is no less than 2.5 page APA format + double space Assignment instruction provided with the f ...
The Szabo vs Reliable Car Parts Corporation fuel pumps Legal Memorandum
Write a Memorandum.Appendix is no less than 2.5 page APA format + double space Assignment instruction provided with the files attached (legal memorandum)Use the files (LM guide+ LM exemplar) to get you know how it will be written. use the file (LM template) to write the paper
MAT 255 Grand Canyon University Probability and Inferential Statistics Questions
Assessment Description1. A patient is classified as having gestational diabetes if their glucose level is above 140 millig ...
MAT 255 Grand Canyon University Probability and Inferential Statistics Questions
Assessment Description1. A patient is classified as having gestational diabetes if their 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+X mg/dl and σ = X+1 mg/dl, where X is the last digit of your GCU student ID number. What is the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:Once?X+1 times, where X is the last digit of your student ID?X+4 times, where X is the last digit of your student ID?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.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 9X percent reliable, gestational diabetes affects X+1 percent of the population in our patient’s age group, and that our test has a false positive rate of X+4 percent. Compute the following quantities based on this new information:If 100,000 people take the blood test, how many people that test positive will actually have gestational diabetes?What is the probability of having the disease given that you test positive?If 100,000 people take the blood test, how many people that test negative despite actually having gestational diabetes?What is the probability of having the disease given that you tested negative?Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?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 of the following:A detailed discussion of your experimental design.How is randomization used in your sampling or assignment strategy?The type of inferential test utilized in your experiment.A formal statement of the null and alternative hypothesis for your test.A confidence interval for estimating the parameter in your test.An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design
5 pages
Solution
Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: The annual income levels and annual expend ...
Solution
Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: The annual income levels and annual expenditure on food and fruits are ...
Cuyamaca Alcoholic Drinks Consumed by Students at A Liberal Arts College HW
PromptIn a previous lab we tested the following hypotheses, H 0: μ = 4.73 and H a: μ < 4.73 (where μ is the mean num ...
Cuyamaca Alcoholic Drinks Consumed by Students at A Liberal Arts College HW
PromptIn a previous lab we tested the following hypotheses, H 0: μ = 4.73 and H a: μ < 4.73 (where μ is the mean number of alcoholic drinks consumed by students at a liberal arts college).In a random sample of 75 students, the mean was 3.93 alcoholic drinks consumed in a week. Here is the StatCrunch output from the hypothesis test.μ: Mean of variableH 0: μ = 4.73H A: μ ≠ 4.73Hypothesis test resultsVariableSample MeanStd. Err.DFT-StatP-valuenumber of drinks per week3.9333333 0.43592434 74 -1.8275343 0.0717 Using this context and the StatCrunch output, explain the meaning of each of the following.
Std. Err (standard error)T-stat (T-score)P-valueIn a previous matched pairs lab we tested the following hypotheses, where μ is the mean of the differences in corn yield for a plot of land (regular seed minus kiln-dried): H0: µ = 0 and Ha: µ < 0. In a random sample of 11 seeds of each type, the mean of the differences in the sample was -33.7. Here is a StatCrunch print-out of the hypothesis test.Paired T hypothesis test:μ D = μ 1 − μ 2: Mean of the difference between Regular seed and Kiln-dried seedH 0: μ D = 0H A: μ D < 0
Hypothesis test resultsDifferenceMeanStd. Err.DFT-StatP-valueRegular seed - Kiln-dried seed-33.72727319.95134610-1.69047610.0609Differences stored in column, Differences.Using this context and the StatCrunch output, explain the meaning of each of the following.
Std. Err (standard error)T-stat (T-score)P-value.
Conditional probabilities
Finding a conditional Probability:
Example
Let's look at a standard deck of 52 cards.
What is the probability of getting 2 ...
Conditional probabilities
Finding a conditional Probability:
Example
Let's look at a standard deck of 52 cards.
What is the probability of getting 2 kings assuming that the first one is not replaced?
4/52 * 3/51 = 1/13*1/17= 1/221
What is the probability of getting 2 kings assuming that the first one is replaced?
4/52 * 4/52 = 1/13 * 1/13 = 1/169
Instructions
Now for your main post do a similar problem using with replacement and without replacement. You can use a card problem as long as it is not 2 kings.
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