Statistics II Midterm Exam2 (1)

.docx

School

Durham College *

*We aren’t endorsed by this school

Course

S21

Subject

Statistics

Date

Apr 3, 2024

Type

docx

Pages

7

Uploaded by JudgeResolve13827

Report
Statistics II Midterm Exam – 100 Marks 6:00 – 9:00 PM Worth: 25% One Sample Hypothesis Test (10 marks) Imagine you are conducting a study to determine whether the average score of students in a particular class is significantly different from the national average score of 75. You collect a random sample of 30 students from the class and find their average score to be 72 with a standard deviation of 8. Perform a one-sample hypothesis test to determine whether the class's average score differs significantly from the national average. Clearly state your null and alternative hypotheses, calculate the test statistic and p-value, and provide a conclusion based on the significance level of α = 0.05. Null hypothesis 1 H0 = 75 2 Alternative hypothesis Ha: 75 3 the critical values are – 2.064 and 2.064. 4 observed test statistics = 1.96 Conclusion there is not sufficient evidence to conclude that the average score of a group of students on standardized test is significantly different from the national average of 75 Two-Sample t Tests and Degrees of Freedom (8 marks) You are investigating whether there is a significant difference in the mean heights of two different populations: Population A and Population B. You collect a random sample of 20 individuals from Population A and find their mean height to be 65 inches with a standard deviation of 3 inches. From Population B, you collect a sample of 25 individuals and find their mean height to be 68 inches with a standard deviation of 4 inches. Conduct a two- sample t-test to determine if there is a significant difference in mean heights between the two populations. Also, calculate the degrees of freedom for this test. The two-sample t-test indicates a significant difference in mean heights between Population A and Population B
Analysis of Variance (ANOVA) and Assumptions (8 marks) Suppose you are analyzing the effectiveness of three different teaching methods (Method A, Method B, and Method C) on improving students' test scores. You collect test scores from three separate groups of students: one group for each teaching method. Conduct an analysis of variance (ANOVA) to determine whether there is a significant difference in mean test scores among the three teaching methods. Also, discuss the assumptions of ANOVA and whether they are met in this scenario. To analyze the effectiveness of three teaching methods on test score use anova. 1 Hypothesis H 0: no difference in mean test scores among methods. H 1: difference exists 2 Assumptions Independence test score is independent. Normality score within each group is normally distributed. Homogeneous of variance: variance of score in each group are equal. 3 Anova: calculate F statistics and p-value. 4 interpreting : Reject H0 if p-value less than 0.05 indicating a significant difference. 5Assumtion check : independence ensure random sampling. Normality: use histograms or normality test Homogeneity of variance: check withing levyne’s test If assumption is violated, consider non-parametric tests like Kruskal-Wallis Type 1 and Type 2 Errors (6 marks) Explain the concepts of Type 1 and Type 2 errors in hypothesis testing. Provide examples to illustrate each type of error. Type 1 error incorrectly rejecting a true null hypothesis example convicting an innocent person in a court trail. Type 2. Error” Failing to reject a false null hypothesis. Example falsely concluding a patient is healthy when they have a disease. Null Hypothesis and Alternative Hypothesis (5 marks)
Define the null hypothesis and the alternative hypothesis. Discuss their roles in hypothesis testing and provide an example of each. null hypothesis (H0): Assumes no difference or effect example the average score is 75. Alternative hypothesis (HA) suggests a difference or effect example the average score. They are used in hypothesis testing to determine if there is enough evidence to reject the null hypothesis in favor of the alternative. Central Tendency and Variability (5 marks) Define central tendency and variability in statistics. Explain how measures such as mean, median, mode, and range are used to describe central tendency and variability in a dataset. central tendency is the typical value in a dataset, while variability measures the spread of the data points. mean Average of all values, influenced by extreme values. Median Middle value when values are sorted, less affected by extremes. Model Most frequent value(s) in a dataset. Range difference between the largest and smallest value indicating data spread. A-Value and Its Representation (5 marks) What does the term "a-value" represent in hypothesis testing? Discuss its significance in decision-making during hypothesis testing and how it relates to the chosen significance level (α). The α-value is the significance level in hypothesis testing, representing the threshold for rejecting the null hypothesis. It is compared to the p-value, with a lower α-value requiring stronger evidence to reject the null hypothesis. The α-value determines the risk of Type 1 errors and guides decision-making in hypothesis testing. One-Tailed vs. Two-Tailed Test of Hypothesis (4 marks) Distinguish between a one-tailed and a two-tailed test of hypothesis. When would you use each type of test, and how does the choice of tails affect the interpretation of the results?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
SEE MORE TEXTBOOKS