Statistics (Ferreria) - First Semester FRQ Review - December 2023

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Los Angeles Pierce College *

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1340

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Statistics

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Feb 20, 2024

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NAME__________________________________________________________________Version Period______________Date______________ AP Statistics Final Practice FRQ Problems FERRERIA STATISTICS ~ 1 ~ 2324 1: Descriptive Statistics Literary scholars sometimes use the distribution of word lengths in a work as a test of authenticity. Below is a frequency table for the word lengths for a random sample of words from F. Scott Fitzgerald’s The Great Gatsby . Word length 1 2 3 4 5 8 10 Frequency 1 4 7 8 3 1 1 (a) Compute the 5-number summary for the word lengths in the sample. Then, use your 5-number summary to create a box plot that summarizes the word length in the sample. (b) Determine if there are any outliers word lengths in the random sample. Show your work. (c) Write a few sentences describing the distribution of word lengths in the sample.

NAME__________________________________________________________________Version Period______________Date______________ AP Statistics Final Practice FRQ Problems (cont.) FERRERIA STATISTICS ~ 2 ~ 2324 2: 2-variable statistics An educator wants to determine whether students' exam scores were related to study time. For example, as students spent more time revising, did their exam score also increase (a positive relationship); or did the opposite happen? The dependent variable for this study was "exam score", measured on a scale from 0 to 100, and the independent variable was "study time", measured in minutes. Predictor Coef SE Coef T P Constant 44.540 xxxxx xxxxx xxxxx Study time (mins) 0.55528 0.05501 10.09 0.000 S = 6.354470 R-Sq = 72.8% R-Sq (adj) = 72.1% (a) What is equation of the least squares regression line? Interpret the slope of the regression in the context of this situation. (b) Explain what the quantity R-sqr = 73.8% measures in the context of this problem. (c) Hyunwoo, a student in the sample, studied for 80 minutes and earned an exam score of 94. Calculate the predicted exam score and the value of the residual for this student.

NAME__________________________________________________________________Version Period______________Date______________ AP Statistics Final Practice FRQ Problems (cont.) FERRERIA STATISTICS ~ 3 ~ 2324 3: Experimental Design Ph ở Real is a new Vietnamese restaurant in Girard, CA that wants to specialize in ph ở , a type of soup. Mai, the owner of Pho Real, wants to test two different preparations for her broth. Four of the Mai’s friends are willing to “be real” and rate the broth on a scale of 1 to 10. (a) Describe how Mai can use a Matched Pair Design to find which broth tastes better. What role does randomization have in this experimental design? (b) Mai would like to perform a “ double-blind ” experiment with her four friends. Explain what “ double-blind ” means in the context of this experiment. Describe how Mai could implement a double-blind experiment. (b) Why would an experiment using 20 subjects in the experiment be better than an experiment with only four subjects?

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NAME__________________________________________________________________Version Period______________Date______________ AP Statistics Final Practice FRQ Problems (cont.) FERRERIA STATISTICS ~ 4 ~ 2324 4: Probability distributions Sapna’s bank tells her that about 2% of all credit card transactions are fraudulent. This worries her because her online business has about 60 transactions per month, and some of them might be credit card frauds! Let X = the number credit card frauds in 60 transactions. (a) Show that distribution of X follows a binomial distribution (Assume that 2% of all transactions are fraudulent) (b) Calculate and interpret the following probabilities: (i) 𝑃(𝑋 = 1) (ii) 𝑃(𝑋 < 2) (iii) 𝑃(𝑋 ≥ 3) Sapna also learns that 24% of her customers use a Mastercard. Let M = the number of Mastercard transactions in 60 transactions. (c) Find the mean and standard deviation for M. (d) Use the Normal approximation for M estimate the probability that 10 or fewer of Sapna’s transactions will be with a Mastercard.

Statistics (Ferreria) - First Semester FRQ Review - December 2023

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