Instructor feed back Phase 1 , some parts of your project were written well. However, I notice some mistakes and I mention some of them: - you didn't mention which are the measures if center and which are the measures of variation - the results concerning the midrange and the standard deviation are not accurate; I would have liked to read more interpretation based on your obtained results - you did not mention that the pacient number is a discrete variable Good luck in the next weeks, Alin Tomoiaga Phase 2 , most part of your work is well written. Unfortunately your computation is not accurate. First of all, the standard deviation of the sample is 8.92. You used the critical values of the normal distribution instead of the ones corresponding to the Student t distribution. You should use them since the variance sigma^2 is unknown. Also, you forgot to divide the standard deviation by sqrt(60). Good luck in the following weeks, Alin Tomoiaga Phase 1, Phase 2, and Phase 3 submissions to make any necessary corrections. Remember if you have questions about the feedback to ask your instructor for assistance. Once you have made your corrections, you will compile your information from Phase 1, Phase 2, Phase 3 and your final conclusion into one submission and submit this as your rough draft for Phase 4 of the course project. Below is a summary of the expectations for Phase 4 of the course project: 1. Introduce your scenario and data set. o Provide a brief overview of the scenario you are given above and the data set that you will be analyzing. o Classify the variables in your data set.  Which variables are quantitative/qualitative?  Which variables are discrete/continuous?  Describe the level of measurement for each variable included in your data set. 2. Discuss the importance of the Measures of Center and the Measures of Variation. o What are the measures of center and why are they important? o What are the measures of variation and why are they important? 3. Calculate the measures of center and measures of variation. Interpret your results in context of the selected topic. o Mean o Median o Mode o Midrange o Range o Variance o Standard Deviantion 4. Discuss the importance of constructing confidence intervals for the population mean. o What are confidence intervals? o What is a point estimate? o What is the best point estimate for the population mean? Explain. o Why do we need confidence intervals? 5. Based on your selected topic, evaluate the following: o Find the best point estimate of the population mean. o Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown.  Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. o Write a statement that correctly interprets the confidence interval in context of your selected topic. 6. Based on your selected topic, evaluate the following: o Find the best point estimate of the population mean. o o Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown.  Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. Write a statement that correctly interprets the confidence interval in context of your selected topic. 7. Compare and contrast your findings for the 95% and 99% confidence interval. o Did you notice any changes in your interval estimate? Explain. o What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain. 8. Discuss the process for hypothesis testing. o Discuss the 8 steps of hypothesis testing? o When performing the 8 steps for hypothesis testing, which method do you prefer; P-Value method or Critical Value method? Why? 9. Perform the hypothesis test. o If you selected Option 1:  Original Claim: The average salary for all jobs in Minnesota is less than $65,000.  Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown. o If you selected Option 2:   o Original Claim: The average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age. Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown. Based on your selected topic, answer the following: 1. Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim. 2. Is the test two-tailed, left-tailed, or right-tailed? Explain. 3. Which test statistic will you use for your hypothesis test; z-test or t-test? Explain. 4. What is the value of the test-statistic? What is the P-value? What is the critical value? 5. 5.) What is your decision; reject the null or do not reject the null? a. Explain why you made your decision including the results for your pvalue and the critical value. 6. State the final conclusion in non-technical terms. 10. Conclusion o Recap your ideas by summarizing the information presented in context of your chosen scenario. Please be sure to show all of your work and use the Equation Editor to format your equations. This assignment should be formatted using APA guidelines and a minimum of 2 pages in length. Name:_Jeff Clayborn_____________________________________ Module 3 Homework Assignment 1. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution or neither. The sample data appear to come from a normally distributed population with σ = 28. Explain. Claim: μ = 977. Sample data: n = 25, 𝑥̅ = 984, s = 25. Explain. Solution: Instructor Comments: Part 1: Since the data comes from a normally distributed population and 𝛔 is known, the hypothesis test involves a sampling distribution of means that is a normal distribution. Part 2: For this, since 𝛔 is unknown, the hypothesis test involves a sampling distribution of means that is a Student t distribution 2. In a sample of 100 M&M’s, it is found that 8% are brown. Use a 0.05 significance level to test the claim that of the Mars candy company that the percentage of brown M&M’s is equal to 13%. Identify the null and alternative hypotheses. Solution: Instructor Comments: Ho: p = 0.13 Ha: p ≠ 0.13 3. (Refer to problem 2) Find the test statistic. Solution: Z statistic = (phat – p)/ √( p* 1-p/n) Z = (0.08 -0.13)/√(0.13*0.87/100) Z = -1.49 Instructor Comments: 4. (Refer to problem 2) Use the Standard Normal Table to find the p-value, critical value(s) and state the decision about the null hypothesis. Solution: Critical values = ± 1.96 P VALUE = 0.1362 Instructor Comments: Since p value is greater than the significance level, we fail to reject the null hypothesis. 5.(Refer to problem 2) State the conclusion in non-technical terms. Solution: Instructor Comments: There is insufficient evidence to reject the claim that the percentage of brown M&M’s is equal to 13%. 6. Test the claim that for the adult population of one town, the mean annual salary is givenby μ= 30,000. Sample data are summarized as n= 17, x = $22,298, and s= $14,200. Use asignificance level of α= 0.05. State the null and alternative hypotheses. Solution: u = 30,000 u ≠ 30,000 7. (Refer to Question 6) Find the test statistic. Solution: T statistic = ( x bar – u)/(s/√n) Instructor Comments: Instructor Comments: T= (22,298 – 30,000)/(14200/ √17) T= -2.236 8. (Refer to Question 6) Find the critical value(s) and state decision about null hypothesis. Solution: Instructor Comments: T critical values = ± 2.12 Since the T statistic lies in the critical region, we reject the null hypothesis. 9. (Refer to Question 6) State the conclusion in non-technical terms. Solution: Instructor Comments: There is sufficient evidence to reject the claim that for the adult population of one town, the mean annual salary is given by μ= 30,000. 10. Find the critical value or values of χ2based on the given information. H1: σ> 26.1, n = 9, α = 0.01 Solution: The critical value = χ2 = 20.09 Instructor Comments: Running head: HYPOTHESIS TESTING 1 Infectious disease hypothesis testing Course Institution HYPOTHESIS TESTING 2 Introduction Hypothesis testing is a statistical process used to test whether there is sufficient statistical evidence to support a claim about a certain population parameter. Steps involved in hypothesis testing include: a) Step 1: formulate a null and alternate hypothesis This step involves determining or predicting what the expected outcome of the research will be. b) Step 2: Determine the significance level ( alpha level) The alpha level gives the probability of committing a type I error. This step thus involves coming up with an appropriate alpha level (maximum allowable error) depending on the topic of investigation. c) Step 3: Data collection and calculation of descriptive statistics This step involving collecting the necessary data required to test the claim and calculating the descriptive statistics. Measures of dispersion and central tendency are useful in calculating the test statistic. d) Step 4: Determine the test to use Hypothesis testing mainly involves use of t tests or z tests. In this step, one determines what test is appropriate to use. Z tests are used when the population standard deviation is known and when the sample size is large. T tests are used when the population standard deviation is unknown and when the underlying population is normally distributed. e) Step5:Determiningthe critical values and the rejection Depending on the test used, one will determine the critical values, depending on whether the test is one tail or two tailed. Based on either the significance level, or critical values one will determine the rejection region HYPOTHESIS TESTING 3 f) Step 6: Calculate the test statistic. For a z test Z statistic = ( x bar – u)/(𝛔/√n) For a t test T statistic = ( x bar – u)/(s/√n) g) Step 7: Determine the p value. Based on the test statistic calculated, one should calculate the p value. h) Step8:Makea decision and state the conclusion In this final step, one makes a decision on whether to reject or not reject the null hypothesis and makes the appropriate conclusion. In an 8 step hypothesis test, one makes use of both critical values and p values to make the statistical decision and conclusion. This ensures that the test was correct done and avoids risk of error. Hypothesis testing for an infectious disease at NCLEX Memorial Hospital In this paper, we will be testing the claim that the average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age. We will be testing this claim at the 0.05 significance level The Null and alternate Hypothesis will be: Ho: u = 65 Ha: u < 65 (claim) This kind of hypothesis testing is a left-tailed hypothesis. This is because in the alternate hypothesis we will be determining whether the mean age is less than 65 years. The p value to check for will be the area on the left tail of the test statistic. For our case, we will use t test. This is because the population standard deviation (𝛔) is unknown. Test statistic HYPOTHESIS TESTING 4 T statistic = ( x bar – u)/ (s/ √n) From the data: Mean (x bar) Standard Error(s/√n) Standard Deviation (s) Count (n) 61.816667 1.1521269 8.9243367 60 T statistic = (61.8167 – 65)/ 1.1521 = -2.763 P value To determine p value we first need to get the degrees of freedom. Degrees of freedom (df) = n – 1 = 60 – 1 = 59 We will then check at t tables for p value associated with the test statistic P (t < -2.763) at 59 df = 0.0038 P value = 0.0038 Critical value To determine the critical value, we need to check t tables for the t value associated with the significance level at the current degrees of freedom. In our case we will check for t value associated with 0.05 left-tail probability at 59 df T critical = -1.671 Critical region = any t value < -1.671 Decision rule and Conclusion We reject the null when p value is less than significance level or when the test statistic lies within the critical region. From the test above, the p value (0.0038) is less than the 0.05 significance level. The t statistic (-2.763) lies in the critical region. Based on this, our decision will be to reject the null hypothesis. We thus conclude that there is sufficient evidence to support the claim that the average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age HYPOTHESIS TESTING Conclusion Hypothesis testing is a great method for determining whether claims about a certain population are statistically significant (valid) or not. 5
Purchase answer to see full attachment