A teacher wants to summarize the exam scores of a class of 50 students to understand the overall performance and variability. The scores (out of 100) are as follows: 75 85 92 88 73 95 80 77 85 90 76 86 93 89 74 96 81 78 86 91 73 83 90 86 71 93 78 75 83 88 77 78 75 85 86 83 90 91 88 90 82 97 79 77 75 80 86 84 85 82 Measures of central tendency class the upper limit of the class frequency (70;75> Mode: (75;80> (80;85> Median: (85;90> (90;95> Population mean: (95;100> Measures of variability Range: Population variance Population standard deviation ##### Sheet/List 2 ##### "A company wants to know if customer preferences for three types of products—Product A, Product B, and Product C—match the market's expected preference distribution. " "They believe that 50% of customers prefer Product A, 30% prefer Product B, and 20% prefer Product C. " They conduct a survey of 200 customers to test this hypothesis. "From the survey, the company records the following observed counts:" Product A: 90 customers Product B: 70 customers Product C: 40 customers Test at the alpha significance level 0.05 "Null hypothesis (H0​): Customer preferences match the expected distribution (50% for Product A, 30% for Product B, and 20% for Product C)." Alternative hypothesis (H1): Customer preferences do not match the expected distribution. Oi (Observed) Ei (Expected) Test criterion Product A 90 Product B 70 Product C 40 ##### Sheet/List 3 ##### "A researcher wants to determine if there is an association between gender and preference for three types of movies: Action, Comedy, and Drama. " "The researcher surveys 200 people, and the data collected is summarized in the table below:" Action Comedy Drama Total Male 40 30 20 Female 10 50 50 Total The goal is to test if there is a significant association between gender and movie preference. Test at the alpha significance level 0.05 Null hypothesis (H₀): Gender and movie preference are independent (no association). Alternative hypothesis (H₁): Gender and movie preference are not independent (there is an association). Expected frequencies Test criterion Action Comedy Drama Action Comedy Drama Male Male Female Female ##### Sheet/List 4 ##### "A nutritionist wants to test whether three different diets—Diet A, Diet B, and Diet C—lead to different average weight loss outcomes. " "To do this, they assign a group of people to each diet and measure their weight loss (in kilograms) after 8 weeks." The nutritionist wants to determine if the diet type significantly affects weight loss. "Null hypothesis (H0): The mean weight loss is the same for all diets, i.e. there is no dependance" Alternative hypothesis (H1​): At least one diet leads to a different mean weight loss. (There is dependance) Test at the alpha significance level 0.05 The weight loss (in kg) for participants in each diet group is as follows: DIET A 4 5 6 5 7 DIET B 8 7 9 8 10 DIET C 3 2 4 3 3 ##### Sheet/List 5 ##### "Suppose a researcher wants to test how two factors—type of fertilizer (Fertilizer X and Fertilizer Y) and sunlight level (Low, Medium, High)—" affect plant growth (measured in centimeters). "Each combination of fertilizer type and sunlight level is tested on one plant (hence, no replication for each combination)." Test at the alpha significance level 0.05 Main Effect of Fertilizer: Whether different types of fertilizer lead to different average growth. H0: No significant difference in plant growth between Fertilizer X and Fertilizer Y. Main Effect of Sunlight Level: Whether different levels of sunlight lead to different average growth. H0: No significant difference in plant growth across different sunlight levels. The researcher collects the following growth measurements (in cm) for each combination of fertilizer type and sunlight level: Sunlight Level Fertilizer X Fertilizer Y Low 12 14 Medium 20 22 High 30 25