Math 1650: Chapters4-6Summary Project

Project:A research group is conducting a study on the effectiveness of a current beta-blocker being used to treat Tachycardia. A study consisting of 300 patients who have been diagnosed with Tachycardia and prescribed this medication participated in the study. As part of the research group you are preparing an analysis on the data set to answer the following research questions.

Research Questions:

1.Is the average pulse rate of a population of 300individuals with the beta-blockersignificantly different from the standard average pulse rate of 72 beats per minute?

2.What proportion of individualswith the Beta-Blockerexhibit a high pulse rate (above 100 bpm), and is this lower than the standard percentage of 10%.

Data Set:Stat Disk; Essentials of Statistics 6^thEdition,Data Set 1: Body Data

Descriptive Statistics:

Conduct a normality assessment:

1.Describe the histogram, does it appear to have a bell-shape?

2.Describe the normal quartile plot, are the data values close to the line?

3.Record the following metrics.(Take values to two decimal points)

a.Mean pulse rate = ________

b.Standard deviation of pulse rate = ________

c.Outliers = ________

4.Is the sample considered normal at the 0.01 significance level.

_________________________________

Normal Distribution:

5.Determine the minimum and maximum usual values for this sample group.

a.How many patients fall above the interval and would be

considered unusually high?

b.How many patients fallbelowthe interval and would be considered unusuallylow?

__________

___________

6.How does this compare to a typical normal distribution where only 5% of the subjects with be outside of two standard deviation?

7.Find the z-score for a pulse rate of 100 bpm._________

8.What probability falls above this z-score? _________

Confidence Intervals:

9.Construct a 95% confidence interval for the mean pulse rate: __________

10.Identify the margin of error: _____________

11.The normal average pulse rate of a population is 72 bpm. Does the confidence interval suggest a mean pulse rate of the group higher, lower, or similar to the 72 beats per minute? Explain.

12.What does the confidence interval suggest about the beta-blocker thesample members are taking fortheir pulsehighrates?

13.High pulse rate is consider being above 100 bpm. Where does this data value fall the with regard to the confidence interval?

14.Draw the confidence interval on the bell-curve provided. Indicate the 72 and 100 bpm values on the graph.

Hypothesis Testing:

Claim:The sample still has a mean pulse rate above72 bpm.

15.Hypothesis: Write the null and alternate hypothesis

16.You will need to conduct a hypothesis test. Checkthe hypothesis test thatis needed. a.Proportion one sample: ______b.Mean one sample: _______c.Standard deviation one sample: ________

17.Conduct a hypothesis Test with a significance level of 0.05:

Statistics	Hypothesis Test Results
ClaimedMean
Test Statistic
Critical Value(s)
P-value

18.Draw the critical region(s) for the hypothesis test.Indicate the test statistic.

19.Based on the P-Value, is the teststatistics significant? Do we reject and fail to reject the null hypothesis?

20.Based on the critical region, is the test statistics significant, do we reject and fail to reject the null hypothesis?

21.State the final conclusion of the hypothesis test.

22.What does the test suggest about the beta-blocker medication the sample members are taking for their high pulse rate?

Binomial Distribution:

Construct a binomial distribution to determine the percentage of people with high pulse rates in a population of people who do not take the medication. Assume a percentage of 10%.

Define threshold:Pulse rate above 100 bpm is considered "high."

Binary variable based on this threshold:

Giventhat only10% of the population develop tachycardiawewill look at the dataas a binomial distribution. Remember, the mean and standard deviation of a binomial distribution are as follows:

23.Using the proportionofadultswith high pulse rates, determine the mean and standard deviation forthe expected valueofadults withhighpulse rates based on the sample 300 adults

24.Describe the meaningof the mean for our sample of 300 adults.

25.Usingtheformula for range of usual values,identifythelimits separating values that are significantly low and significantly high.

26.Describe the meaning of the usual value rangefor a sample of 300 adults.

27.Determine the number of subjects inyour sample data that would be considered to havea high pulse rateusing the definition given at the beginning of the project.Refer to the information above to determine what values are considered to be high pulse rates.

28.Based on your results, would the number of subjects inyour data set withhigh pulse rates be significantly low, significantly high, or neither.Justify your reasoning.

29.Find the probability of exactlythe number of people inthesample with high pulse rates.

Identify your sample size, probability of success, and x value Also, Identify the column and the probability given. Describe what the probability tells us about our data set

Sample size =

Probability of success =

x value =

Column =

Probability =

30.Does this analysis suggest or fail to suggest that thebeta -blockerhasreduced the number ofpeoplewithhigh pulse rates?

Overall Summary:

Research Questions:

3."Is the average pulse rate of a population of 300 individuals significantly different from the standard average pulse rate of 72 beats per minute?

4.What proportion of individuals exhibit a high pulse rate (above 100 bpm), and is this lower than normal?