midterm 1 review packet(1)

Spring 2023 - Statistical Methods Midterm 1 Review Problem 1. Pet Owner (W) Job Salary (X) Stress Level (Y) Body Fat % (Z) Alexa Yes 200,000 100 65 Bobby No 125,000 85 55 Hank No 55,000 60 24 Veronica Yes 165,000 40 39 Roberto Yes 75,000 90 20 Find the following: a) w 2 = b) y 4 = c) x 5 = d) Circle the correct answer: 65 = w 1 y 3 z 4 z 1 Problem 2. Below are the descriptions of different types of variables In the blank beside each description, write whether the type of variable being described is continuous, discrete, ordinal, categorical, or dichotomous ___________________________ Numeric values that are whole numbers only ___________________________ Number of brothers and sisters ___________________________ Two or more distinct categories ___________________________ Height, Weight, Age ___________________________ Values that indicate rank or order ___________________________ Survival Outcome (Yes, No) ___________________________ Place of residence (Texas, California, Colorado) ___________________________ Numeric values that have an infinite number of possible values ___________________________ Variable with only two categories ___________________________ Position in a race (1 st , 2 nd , 3 rd )

Problem 3. The frequency table below shows the number of Congressional seats in each state in the United States. Fill out all blank white cells in the table. Round your answers to the second decimal place if needed. No. of Seats in the US House of Representative Width of Interval Frequency (# of states) Percent in interval (Area) Density (% per unit) Height 0-3 15 3-10 23 10-20 8 20-60 4 TOTAL Use the data in the frequency table to construct a Density Histogram.

Problem 5. A personality researcher is interested in the extraversion scores of college students. Below are the extraversion scores of a sample of college students studied by this researcher. Fill in all blank spaces in the table. Round to the second decimal place if necessary. Raw Score Deviation Squared Deviation   18   20   21   16   20   17   22   26 Mean 20 Standard Deviation: Problem 6. Calculate the standard deviation and z-scores for the raw scores below and fill in all other blank cells in the table. Round to the second decimal place if necessary. X Deviations Squared Deviations Z-Scores 15 11 24 22 19 17 20 8 Mean SD

Problem 7. The MCAT is an admissions test given to applicants who have applied to enter medical school. Among pre-med students at a certain university, scores on the MCAT were normally distributed with an average of 506 and an SD of 44. Answer the following questions about these students. Round z-scores to the second decimal point (Example: 1.032 should be rounded to 1.03). Round percentiles to the nearest whole percent (Example: 13.7% should be rounded to 14%). a) A student scored 524 on the MCAT. What was this student's z-score? b) A student scored 524 on the MCAT. What was this student’s percentile? c) To be at the 50 th percentile of the distribution, a student needed an MCAT score of around __________ points Problem 8. Fill in the blanks in the table below by making transformations. The mean is 1020 and the standard deviation is 320. The distribution is normal. Round z-scores to the second decimal point (Example: 1.032 should be rounded to 1.03). Round percentiles to the nearest whole percent (Example: 13.7% should be rounded to 14%). Raw Score Z-Score Percentile 1340 -2.00 50% 620 1.75 96% 4% 1148 -0.90 90%

Problem 10. Below are the hourly wages for three students. Using the data for Problem 9 (Mean = $11, SD = $3), calculate the students’ z-scores and percentiles and write them in the table below. Round z-scores to the second decimal point (Example: 1.032 should be rounded to 1.03). Round percentiles to the nearest whole percent (Example: 13.7% should be rounded to 14%). Additionally, label where these students fall on the distribution you have drawn above. Student raw score z-score percentile Aziz $9.00 Elizabeth $18.00 Aliana $3.50 Problem 11. Fill in the blanks for the following statements. 1. In a ______________________ skewed distribution, the mean is greater than the median. 2. In a __________________________ distribution, the mean and the median are the same. 3. In a negatively skewed distribution, the ____________ is less than the ______________. 4. The average of the deviations and z-scores should always be ________________. 5. The ___________________ and ______________________, are descriptive statistics.