Final Exam Practice Problems (1)

STAT 201 Final Exam Practice Problems 1. Suppose the percentage of all students on your campus that own a car is 48.2%. Suppose a sample of 100 students is obtained and from this sample we find that 46% own a car. a. What type of variable was collected? b. Identify the sample and population. c. Identify the statistic and the parameter. 2. Identify the following as either categorical or quantitative. If it is quantitative identify it as either continuous or discrete. Identify the types of graphs that could be used to represent these variables. Identify whether you would use proportions or means to study the variable. a. gender. b. Temperature. c. Number of days during the past week that a college student aged 21 years or older has had at least one drink. d. Zip code. 3. The following is a random sample of the number of points scored by the USC football team in 9 games of the 2018 season: 10 10 13 15 17 26 28 34 48 Note: ∑ x = 201 ∑ ( x −´ x ) 2 = 1314 The following is a random sample of the number of points scored by the Clemson football team in 8 games of 2018 season: 6 24 28 31 34 38 38 47 Note: ∑ x = 246 ∑ ( x −´ x ) 2 = 1045.5 **** In addition to being able to calculate these values you will be asked to interpret them. Note you will not have to write out an interpretation of these measurements on the exam but you do need to know what they represent (their definitions) for multiple choice type questions. ******************************************************* a. Find and interpret the mean number of points scored by both teams and comment on any differences. b. Find and interpret the mode number of points scored by both teams. c. Find and interpret the range for the number of points scored by both teams and comment on any differences. d. Find and interpret the standard deviation for the number of points scored by both teams and comment on any differences. e. Find and interpret the five number summary for the number of points scored by both teams. f. Create boxplots for the two different datasets and comment on the differences between the two datasets. Comment on the shape of the distributions based on the boxplots. g. Comment on the shape of the distributions by comparing the mean and the median values. h. If the highest number of points scored by USC was 77 (not 48) which of the following measurements would be influenced? In other words, which measurements are not resistant. i. Mean ii. Median iii. Mode iv. Range v. Standard deviation vi. Min vii. Q1 viii. Q3 ix. Max x. IQR 4. The following data represent the number of days absent, x, and the final grade, y, for a sample of college students in a general education course at a large state university. # of absences 0 1 2 3 4 5 6 7 8 9 Final Grade 89. 2 86. 4 83. 5 81. 1 78. 2 73. 9 64. 3 71. 8 65. 5 66. 2 Simple linear regression results: Dependent Variable: Final Grade Independent Variable: # absences Final Grade = 88.73 - 2.83 # absences Sample size: 10 R (correlation coefficient) = -0.947395 R-sq = 0.8976 Estimate of error standard deviation: 3.0673204 Parameter estimates:

ParameterEstimate Intercept 88.73 Slope -2.83 a. Based on the scatter plot given what can you state about the relationship between the number of days absent and the final grade. b. Based on the information given what do we know about the correlation coefficient. (would it be negative or positive) c. Give the prediction equation for this data. d. Interpret the slope and y-intercept. e. Predict the final grade for a student who misses five class periods. f. Would it be reasonable to use the prediction line to predict the final grade for a student who has missed 15 class periods? Why or why not? g. Give and interpret the value of r 2 . (you will not have to write out the interpretation on the exam but you will need to know the definition for a possible multiple choice question). 5. The local golf store sells an “onion bag” that contains 35 “experienced” golf balls. Suppose that the bag contains 20 Calloways, 8 Maxflis, and 7 Top-Flites. Suppose you are going to randomly select two golf balls from the bag without replacement. Use a tree diagram to answer the following: a. Fill in all with the correct options (use C for Calloways, M for Maxflis, and T for Top-Flites) and all with the correct probabilities for each branch. b. State the sample space. c. What is the probability that two randomly selected golf balls are both Calloways? (Round to 4 decimals) d. What is the probability that the first ball selected is a Calloway and the second is a Maxfli? (Round to 4 decimals) e. What is the probability that one golf ball is a Calloway and the other is a Maxfli? (Round to 4 decimals) 6. The following data represent political party by age from an entrance poll during the Iowa caucus (2008 Democratic Primary): 17-29 30-44 45-64 65+ Total Republican 224 340 1075 561 2200

a. Construct a 99% confidence interval for the population mean number of books that Americans read during the past year. Interpret the interval. i. Calculate the point estimate. ii. Determine the critical value. iii. Calculate the standard error. iv. Calculate the margin of error. (round to 2 decimal places) v. Calculate the confidence interval. (round to 2 decimal places) vi. Interpret the interval. vii. If we were to decrease the level of confidence would the interval get wider or narrower? viii. If we were to decrease the number of samples taken would the interval get wider or narrower? b. Is there evidence at the 0.01 level of significance that the mean number of books that Americans read during the past year is greater than 13 books? Do all steps of the hypothesis test but note that the p-value is 0.0543 i. State the hypotheses. (must use the correct notation). ii. Calculate the appropriate test statistics. iii. State your decision. iv. Interpret your results in the context of the problem. c. Comment on the connection between the confidence interval and the hypothesis test. 13. An observation study was conducted where the hand-washing behavior of 6000 adults as inconspicuously observed within public rest rooms (selected at random). It was observed that 4620 adults were observed washing their hands. a. Construct a 95% confidence interval for the population proportion of adults who wash their hands in public rest rooms. Interpret the interval. i. Calculate the point estimate. (round 2 decimal) ii. Determine the critical value. iii. Calculate the standard error. (round 4 decimals) iv. Calculate the margin of error. (round 2 decimals) v. Calculate the confidence interval. vi. Interpret the interval. b. Is there evidence at the 0.05 level of significance that the proportion of adults who wash their hands in public rest rooms is different than 78.5%? i. State the hypotheses. (must use the correct notation). ii. Calculate the appropriate test statistics. iii. Calculate the p-value. iv. State your decision. v. Interpret your results in the context of the problem. c. Comment on the connection between the confidence interval and the hypothesis test. 14. A researcher randomly selected 11 individuals (and their cars) to participate in a study to determine if higher-octane fuels result in better gas mileage for their cars. Each car was given 10 gallons of 87 octane gas and the miles driven until the car ran out of gas was recorded. Each car was also given 10 gallons of 92 octane gas and the miles driven until the car ran out of gas was recorded. The results were as follows and the statcrunch output is provided. Note that each car was given both fuels and values were recorded for both. Drivers 1 2 3 4 5 6 7 8 9 10 11 Miles on 87 Octane 234 257 243 215 114 287 315 229 192 204 547 Miles on 92 Octane 237 238 229 224 119 297 351 241 186 209 562 μ 1 = mean of the miles per gallon for 92 Octane fuel. μ 2 = mean of the miles per gallon for 87 Octane fuel. a. Are the two samples dependent or independent samples? b. What is the correct test to use? Paired-t test; two-sampled t c. Set up the correct hypotheses needed to test the claim that the mean gas mileage using the 92-octane fuel was higher than the mean gas mileage using the 87-octane fuel. d. Use the output from Excel to state the findings of the hypothesis test. You must state the decision and then interpret the results in the context of the problem. Use a level of significance of 0.05. Test Statistic = 1.16 P-value = 0.1414 e. Use the output from Excel to answer the following questions about the confidence interval. 95% confidence interval was found to be (-4.90, 15.08) i. Which group had a higher mean mileage per gallon? Justify your answer.

ii. Is there evidence, based on the confidence interval, that there is a difference in the miles per gallon based on the octane of the fuel? Justify your answer. 15. A curriculum specialist is interested in whether instruction method A or instruction method B results in a greater mean score on a standardized test. A random sample of 23 students are taught using method A and a random sample of 21 students are taught using method B. μ 1 = mean score for instruction method A μ 2 = mean score for instruction method B a. Are the two samples dependent or independent samples? b. What is the correct test to use? Paired-t test; two-sampled t test c. Set up the correct hypotheses needed to test the claim there is a difference in the mean score on a standardize test between the two methods. d. Use the output from Excel to state the findings of the hypothesis test. You must state the decision and then interpret the results in the context of the problem. Use a level of significance of 0.05 Test Statistic = -2.31 P-value = 0.0263 e. Use the output from Excel to answer the following questions about the confidence interval. 95% confidence interval was (-18.68, -1.24) i. Which group had a higher mean score? Justify your answer. ii. Is there evidence, based on the confidence interval, that there is a difference in the mean score? Justify your answer.