University:
Florida Gateway College
Course:
MAC 2312 | Calculus II
Academic year:

2024
Views:

475

Pages:

4
Author:

Ruby Bates

Question 1 The measures which give you the spread of the data values are: a. Measures of location b. Measures of dispersion c. Measures of central tendency d. Measures of percentiles Answer: The correct answer is b) Measures of dispersion. Measures of dispersion quantify the spread, variability, or distribution of data values around a central tendency. Examples include range, variance, and standard deviation. Question 2 Discuss the coefficient of variation (CV) and explain why it is used. Answer: Definition: CV is a measure of dispersion that indicates the extent of variability in relation to the mean. 𝐶 𝑉 = 𝜎 𝜇 CV= μ σ where 𝜎 σ is the standard deviation, and 𝜇 μ is the mean. Purpose of CV: It allows comparison of the relative variability of data from different datasets or contexts. It is particularly useful when the means of datasets are different, as it normalizes variability relative to the mean. For example, if Sample 1 has 𝐶 𝑉 = 15 % CV=15% and Sample 2 has 𝐶 𝑉 = 20 % CV=20%, Sample 2 shows more variability relative to its mean. Question 3 Given data: 𝑛 = 157 , 𝑥 ˉ = 146 mmHg , 𝑠 = 27 mmHg , 𝛼 = 0.01 n=157, x ˉ =146mmHg,s=27mmHg,α=0.01 Test if the mean systolic blood pressure for African-American men is greater than 140 mmHg. Answer: Hypotheses: 𝐻 0 : 𝜇 ≤ 140 (Null hypothesis) 𝐻 𝑎 : 𝜇 > 140 (Alternative hypothesis) H 0 :μ≤140(Null hypothesis)H a :μ>140(Alternative hypothesis) Test statistic: 𝑡 = 𝑥 ˉ − 𝜇 𝑠 / 𝑛 = 146 − 140 27 / 157 = 2.78 t= s/ n x ˉ −μ = 27/ 157 146−140 =2.78 p-value: Using 𝑡 t-distribution: 𝑝 -value = 0.0031 p-value=0.0031 Conclusion: Since 𝑝 < 𝛼 ( 0.0031 < 0.01 ) p<α(0.0031<0.01), we reject 𝐻 0 H 0 . There is sufficient evidence to conclude that the mean systolic blood pressure is greater than 140 mmHg at a significance level of 0.01. Question 4 Probability of drawing a square pyramid from the box: Total shapes = 6 + 4 + 12 + 14 = 36 6+4+12+14=36. Probability of square pyramid: 𝑃 ( square pyramid ) = 12 36 = 1 3 P(square pyramid)= 36 12 = 3 1 Answer: The correct option is c) 1 3 3 1 . Question 5 Scatter plot and correlation statement: Correct option: 2) "There is a weekly positive correlation between 𝑋 X and 𝑌 Y." Explanation: A scatter plot helps visualize the relationship between 𝑋 X (independent variable) and 𝑌 Y (dependent variable). A correlation coefficient of 𝑟 = 0.099 r=0.099 indicates a weak positive correlation.