Review_Final Exam_Fall 2023 - Tagged

1 Review Questions for Final Exam PSYC 1303 Statistical Methods. Fall 2023. 1. What kind of variable is "Favorite Candy"? (Chapter 2, Section 2) A. Discrete B. Categorical C. Dichotomous D. Continuous 2. What kind of variable is "age" (Chapter 2, Section 2) A. Discrete B. Categorical C. Dichotomous D. Continuous 3. How many values does a dichotomous variable have? (Chapter 2, Section 2) 4. Indicate whether the following variables are numeric or nominal. (Chapter 2, Section 2) a) Discrete ___________ b) Categorical __________ c) Dichotomous __________ d) Continuous ___________ 5. A negatively skewed distribution has .... (Chapter 2, Section 6) A. A long tail pointing to the right B. A long tail pointing to the left C. Equal tails on both sides 6. In a symmetric distribution, what is the z-score of the median? (Chapter 3, Section 2; Chapter 4, Section 2) 7. In a normal distribution, what percentage of scores lie between z = -2.00 and z = 2.00? (Chapter 4, Section 5) 8. If height is normally distributed and Salvador has a z-score of -1.00 for height, what is Salvador's percentile? (Chapter 4, Section 5)

2 9. Describe the relationship between the mean and the median for each of the distributions below. Use the following symbols to describe the relationship: < , > , or = For example: Four > Two Distribution 1: ___________________________________________________ Distribution 2: ___________________________________________________ Distribution 1 Distribution 2

4 11. If a raw score is below the mean and its Distance from the Mean is 7, what is its Deviation? (Chapter 3, Sections 3 & 4) 12. If the mean is 120 and Teresa's raw score is 105, what is her Deviation? (Chapter 3, Section 4) 13. The Standard Deviation of IQ scores is 15. What is the Variance? (Chapter 3, Section 5) 14. High school students spend an average of 1200 hours per year on the internet, with a standard deviation of 150 hours. The number of hours spent on the internet is normally distributed. (Chapter 4, Sections 3-6) a) If Elida's z-score is 1, how many hours does she spend on the internet? b) What is Elida's percentile? Round to nearest whole percentile. [Example: 37%] c) If Carlos spends 1,425 hours per year on the internet, what is his deviation from the mean? d) What is Carlos' z-score ? Round to two decimal places. [Example: 3.25] e) What is Carlos' percentile? Round to one decimal place .[ Example: 74.1% ]

5 15. For the raw scores below, calculate the mean, deviations, squared deviations, variance and standard deviation. (Chapter 3, Sections 4 and 5) Raw score Deviation Squared Deviation 14 ___________ ___________ 24 ___________ ___________ 12 ___________ ___________ 35 ___________ ___________ 28 ___________ ___________ 31 ___________ ___________ Mean: ___________ Variance: __________[Round to two decimal places. Example: 38.33] Standard Deviation: __________ [Round to two decimal places. Example: 6.19]

7 17. Santa leaves candy for nice children, but lumps of coal for naughty ones. Are the following correlations positive or negative? (Chapter 6, Section 1) (a) Correlation between how naughty a child is Positive Negative and how nice the child is. (b) Correlation between how naughty a child is Positive Negative and how much candy Santa leaves. (c) Correlation between how naughty a child is Positive Negative and how much coal Santa leaves 18. If the correlation of two variables is -.80, how strong is their relationship? (Chapter 6, Section 2) (a) Weak (b) Moderate (c) Strong (d) Very strong (e) Something's wrong 19. If the correlation of two variables is .10, how strong is their relationship? (Chapter 6, Section 2) (a) Weak (b) Moderate (c) Strong (d) Very strong (e) Something's wrong 20. If the correlation of two variables is 2.30, how strong is their relationship? (Chapter 6, Section 2) (a) Weak (b) Moderate (c) Strong (d) Very strong (e) Something's wrong 21. The point (Z x , Z y ) is on the Positive Z-Equal Line. If Z x = 1.00, what is the value of Z y ? (Chapter 5, Section 8) (a) r* Z x (b) 1.00 (c) -1.00

8 22. The point (Z x , Z y ) is on the Regression Line. If Z x = 1.00, what is the value of Z y ? (Chapter 7, Section 6) (a) r* Zx (b) 1.00 (c) -1.00 23. At fast-food restaurants in San Diego, California, the average number of hamburgers sold per week is 2,500, with a standard deviation of 300. The average number of sodas sold per week is 4,000, with a standard deviation of 500. The correlation between hamburger sales and soda sales is .75. a) If a restaurant's z-score for hamburger sales is 1.60, what is the restaurant's estimated z-score for soda sales? [Round z-score to two decimal places. Example 1.58] (Chapter 7, Section 6) b) If a restaurant's z-score for hamburger sales is 0.00, what is the restaurant's estimated z-score for soda sales? (Chapter 7, Section 6) c) If a restaurant's hamburger sales are at the 80 th percentile, what is the estimated percentile for the restaurant's soda sales? (Chapter 7, Section 7) [Round the percentile to one decimal place. Example 29.2%] d) If a restaurant's hamburger sales are at the 33 rd percentile, what is the estimated percentile for the restaurant's soda sales? (Chapter 7, Section 7) [Round the percentile to one decimal place. Example 29.2%]

10 24. The mean of a list of 10 numbers is 6 with a SD of 2. If you add 3 to each value in the list, what will be the new values for the mean and SD? (Chapter 6, Section 5) a) Mean=6; SD=2 b) Mean=6; SD=5 c) Mean=9; SD=2 d) Mean=9; SD=5 e) It cannot be determined without the raw data 25. The mean of a list of 10 numbers is 15 with a SD of 6. If you divide each value in the list by 3, what will be the new values for the mean and SD? (Chapter 6, Section 6) a) Mean=15; SD=6 b) Mean=15; SD=2 c) Mean=5; SD=6 d) Mean=5; SD=2 e) It cannot be determined without the raw data 26. Suppose the correlation between x and y is .72. (Chapter 6, Section 8) a) What is the new correlation if you subtract 2 from all the values of y? b) What is the new correlation if you divide all the values of y by -3?

11 27. The table below shows the number of times that five teenagers went skateboarding during the past month and the number of miles they traveled on their skateboards. Complete the empty values in the table (SDs, z-scores, cross-products and r). Hint: Check your work. The correct value of the correlation is greater than 0.58 but less than 0.66. (Chapter 6, Section 3) Cross- Product Teenager No. times skateboarding (x) Miles (y) No. times skateboarding (x) Miles (y) No. times skateboarding (x) Miles (y) No. times skateboarding (x) Miles (y) 1 12 34 -5 -15 25 225 2 22 94 5 45 25 2025 3 17 64 0 15 0 225 4 2 4 -15 -45 225 0 5 32 49 15 0 225 2025 MEAN 17 49 r = SD Squared Deviations Z-scores Raw Data Deviations

13 31. Jenny bought her daughter the Jelly Belly BeanBoozled game and put all the jellybeans into a glass jar as a joke. BeanBoozled is a candy game where the flavors of the beans are either tasty (e.g. coconut, peach, lime) or disgusting (e.g. spoiled milk, barf, grass clippings). Importantly, the tasty beans look exactly like the disgusting beans, so you don’t know what you’ll be eating until you bite into it! Let us assume that there are 120 total jellybeans in the jar. The breakdown of flavors is as followed: 15 coconut, 20 peach, 35 lime, 10 grass clippings, 25 barf, and 15 spoiled milk. Jenny mistakenly forgot that the jar was full of BeanBoozled candy and grabbed a jellybean from the jar. a) What is the probability that Jenny will eat a disgusting flavor? Disgusting flavors are barf, spoiled milk, and grass clippings. (round to two decimal points) (Chapter 8, Section 1) b) What is the probability that Jenny will eat a coconut jellybean? (Chapter 8, Section 1) c) What is greater: the probability of eating a tasty flavor or a disgusting flavor? (Chapter 8, Section 1) 32. A University Health Center is interested in how many students stay up late cramming for final exams. A pollster from the health center obtains a list of students, randomly selects 500 of them and finds that 375 students from the sample stay up late cramming for final exams. In actuality, the entire student body is 23,850 and of these 12,640 stays up late cramming for final exams. (Chapter 9, Section 1) a) What is the population of interest in this example? b) What is the size of the population? c) What is the size of the sample? d) What is the value of p? (round to two decimal points) e) What is the value of π? f) What is the sampling error for this poll?

14 33. A reporter for the North Pole newspaper interviews four samples of voters to see how many people want holiday music to start playing on the local radio stations as of November 1 st . Each sample has 5 voters. The results are shown below. A 1 indicates that the voter wants holiday music to play starting November 1 st and a 0 indicates that the voter does not want holiday music to play starting November 1 st . (Chapter 9, Section 2) Sample 1 Sample 2 Sample 3 Sample 4 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 a) What is the value of N? b) What is the value of k? c) For each sample, calculate p (the proportion of people who want holiday music to start playing November 1 st ) d) For each sample, calculate q. e) In actuality, 90% of North Pole residents want holiday music to start playing on November 1 st . Use this information to find the sampling error for each of the four samples above. f) Find the standard deviation for each sample. (round to two decimal points) (Chapter 10, Section 1)

16 35. An up and coming social media app wants to know the average amount of time people spend on their phones so they can adjust the amount of advertisements they show their users. A researcher for the app randomly selects 1600 users and measures the amount of time they spend on their phones. The research finds that on average people spent 5 hours on their phones with an SD of 2.5 hours. The true average amount of time all people spend on their phones is 3 hours with a SD of 1 hours . (Chapter 10, Section 5) a) What is the sample mean of X? b) What is the population mean of X? c) What is the sampling error? d) What is the SD? e) What is σ? f) Assume we do not know true values. Construct the 95% Confidence Interval for average time spent on the phone. (hint: we know the sample mean and are looking for likely values of the population mean)

17 36. A baker is interested in finding out whether her chocolate chip cookies taste better than her sugar cookies. To test this, the baker designs a two-group study. One group eats and rates the chocolate chip cookies and another group eats and rates the sugar cookies. The mean tastiness of the chocolate chip cookies was 6 and the mean tastiness of the sugar cookies was 8. The baker (and part time statistician) calculates that the SE X 1 − X 2 = 1.5. (Chapter 11, Section 3) a) What is the null hypothesis for this example? b) What is the alternative or substantive hypothesis for this example? c) What is the X 1 - X 2 d) What is t for the difference between the samples? e) Is the observed t value in the critical region for the 5% of unlikely scores? f) What should the baker conclude about the null and alternative hypotheses? 37. What are the definitions of a Type I and Type II error? (Chapter 11, Section 4; Chapter 12, Sections 1 & 2)

19 Word bank: Symbols / formula: Answer: A. Alternative Hypothesis. B. Formula for the standard deviation of a Bernoulli variable. C. Null Hypothesis. D. General formula of a line. E. Short formula for RMS error of a regression . F. Formula for 95% CI for sample means G. Formula for a standardized regression line (z-score form). H. Formula for 95% CI for probabilities. I. Simplified way to calculate r. J. Formula for the Standard Error of sampling distribution. K. Symbol for the correlation coefficient. L. Formula for Prediction Error. M. Symbol for the proportion in a population. N. Formula for t-value. O. Unstandardized point of averages P. Formula for the Standard Deviation. Q. Formula for the slope of an unstandardized regression line (raw score form). R. Formula for z-scores. S. symbol for Standard Deviation in a population . ^ σ √ N π H 0 : μ 1 = μ 2 ;μ 1 − μ 2 = 0 √ p ∗( 1 − p ) Z y = r ×Z x rawscore − mean SD ( r ∗ S D y S D x ) e = y − ŷ ° √ mean of squareddeviations √ 1 − r 2 ×S D y r H 1 : μ 1 ≠ μ 2 ( x 1 − x 2 ) − E ( x 1 − x 2 ) S E x 1 − x 2 y = slope ∗ x + intercept Average Cross Product of the z-scores p± 2 ∗ SE p σ X ± 2 ∗ SE X ( x , y )