Virtual Course MATH 250 Elements of Statistics Probelms
KnowledgeCatsvirtual_course_math_250_elements_of_statistics_probelms.xlsx
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Sample Test Questions | NAME: | |||||||||||||
Virtual Course MATH 250 Elements of Statistics | ||||||||||||||
Multiple Choice. Choose the one best answer, placing that answer to the left of the question's number. Work should be shown out to the right of the question as needed. Hypothesis testing templates are provided on the next worksheet. | ||||||||||||||
1. | The editors of Celebrity Statistics magazine wish to determine Americans’ favorite celebrities. A ballot is included in the November issue of the magazine. Readers are encouraged to mail in their ballots. Indicate the population and sample. | |||||||||||||
A. | Population: Readers of Celebrity Statistics | |||||||||||||
Sample: Readers who mail in their ballots | ||||||||||||||
B. | Population: Readers who mail in their ballots | |||||||||||||
Sample: Readers of Celebrity Statistics | ||||||||||||||
C. | Population: Readers who mail in their ballots | |||||||||||||
Sample: Americans | ||||||||||||||
D. | Population: Americans | |||||||||||||
Sample: Readers who mail in their ballots | ||||||||||||||
2. | What percent of hospital patients were at most 49 years old? | |||||||||||||
Ages | Frequency | |||||||||||||
A. | 70.8% | 0-9 | 3 | |||||||||||
B. | 60.4% | 10-19 | 3 | |||||||||||
C. | 39.6% | 20-29 | 4 | |||||||||||
D. | 29.2% | 30-39 | 4 | |||||||||||
40-49 | 5 | |||||||||||||
50-59 | 7 | |||||||||||||
3. | Within which age group would the third quartile (Q3) fall? | 60-69 | 9 | |||||||||||
70-79 | 8 | |||||||||||||
A. | 50-59 | 80-89 | 3 | |||||||||||
B. | 60-69 | 90-99 | 2 | |||||||||||
C. | 70-79 | |||||||||||||
D. | 80-89 | |||||||||||||
4. | Consider the following stem-and-leaf plot displaying ACT scores. In the plot, 1|2 represents a score of 12. Which of the following is false with regard to the data in this stem-and-leaf plot? | |||||||||||||
1 | 2334 | |||||||||||||
A. | There were 29 pieces of data collected | 1 | 57888899 | |||||||||||
B. | The range of this data set is 23 | 2 | 000112223 | |||||||||||
C. | The median of this data set is 21 | 2 | 55567 | |||||||||||
D. | The mode for the data set is 18 | 3 | 23 | |||||||||||
3 | 5 | |||||||||||||
5. | A state politician wants to gauge public opinion in his area before deciding to run for re-election. For the study, 200 registered voters are chosen at random from each county in his district. What type of sampling is being utilized? | |||||||||||||
A. | Cluster Sampling | |||||||||||||
B. | Stratified Sampling | |||||||||||||
C. | Systematic Sampling | |||||||||||||
D. | Simple Random Sampling | |||||||||||||
The following data shows the weights of 12 randomly selected newborn babies. | ||||||||||||||
6.8 | 9.1 | 8.7 | 7.5 | 8.2 | 5.4 | 6.5 | 8.5 | 7.3 | 6.6 | 5.9 | 7.3 | |||
6. | Find the mean and median to the nearest hundredth for this sample data. | |||||||||||||
A. | mean = 7.32, median = 7.30 | Mean = | 7.32 | |||||||||||
B. | mean = 7.30, median = 7.32 | Median = | 7.30 | |||||||||||
C. | mean = 7.50, median = 7.48 | |||||||||||||
D. | mean = 7.48, median = 7.508 | |||||||||||||
7. | Which of the following gives the sample standard deviation and the range of the sample data? | |||||||||||||
A. | SD: 1.10; Range: 1.8 | Std Dev = | 1.15 | |||||||||||
B. | SD: 1.15; Range: 3.7 | Range = | 3.70 | |||||||||||
C. | SD: 1.10; Range: 3.7 | |||||||||||||
D. | SD: 1.15; Range: 1.8 | |||||||||||||
8. | Which one of the following describes a quantitative, continuous variable? | |||||||||||||
A. | Classification of students (freshman, sophomore, junior, senior) | |||||||||||||
B. | Lengths of fish caught in a lake | |||||||||||||
C. | Hair color | |||||||||||||
D. | Number of students in a class. | |||||||||||||
Exam Scores for Two 5th Grade Student Groups | ||||||||||||||
9. | Which distribution shape best describes the boxplot for Class 5A? | |||||||||||||
A. | Bell shaped | |||||||||||||
B. | Uniform | |||||||||||||
C. | Skewed right | |||||||||||||
D. | Skewed left | |||||||||||||
10. | Which of the following statements is true concerning the box-and-whisker plots? | |||||||||||||
A. | Class 5A has a larger range than Class 5B | |||||||||||||
B. | Class 5A has a larger interquartile range (IQR) than Class 5B | |||||||||||||
C. | Class 5A has a larger median than Class 5B | |||||||||||||
D. | Class 5A has a larger maximum value than Class 5B | |||||||||||||
11. | Out of twenty randomly chosen college students, at least 8 owned a tablet. What is the complement of this description? | |||||||||||||
A. | Eight or fewer owned a tablet | |||||||||||||
B. | Fewer than eight owned a tablet | |||||||||||||
C. | No more than eight owned a tablet | |||||||||||||
D. | Eight or more owned a tablet | |||||||||||||
12. | If P(A)=0.03, which one of the following statements is false? | |||||||||||||
A. | The probability of the complement of A is 0.97. | |||||||||||||
B. | The probability of event A happening twice in a row (with replacement) is 0.0009. | |||||||||||||
C. | Event A is an “unusual” event | |||||||||||||
D. | For each 3 times event A happens, there are 100 times in which A doesn’t happen. | |||||||||||||
13. | A bag contains 3 red marbles, 9 blue marbles, and 5 green marble. If you draw two marbles, one right after the other and without replacement, what is the probability that they will both be blue? | |||||||||||||
A. | (9/17) * (8/16) | |||||||||||||
B. | (9/17) + (8/16) | |||||||||||||
C. | (9/17) * (8/17) | |||||||||||||
D. | (9/17) + (8/17) | |||||||||||||
The following table is the probability distribution for the number of courses taken by FHSU students in a certain semester. In the table, x = the number of courses taken, and P(x) = the probability of taking x courses. | ||||||||||||||
14. | The probability that a randomly selected student takes at least 3 courses is: | |||||||||||||
A. | 0.151 | |||||||||||||
B. | 0.249 | |||||||||||||
C. | 0.600 | |||||||||||||
D. | 0.849 | |||||||||||||
15. | Determine the expected number (mean) of courses taken by students. | |||||||||||||
A. | 0.2 | |||||||||||||
B. | 0.7 | |||||||||||||
C. | 3.0 | |||||||||||||
D. | 3.5 | |||||||||||||
16. | 40% of all people have blood type A. What is the probability of randomly selecting 2 people and neither of them has blood type A? | |||||||||||||
A. | 1.20 | |||||||||||||
B. | 0.80 | |||||||||||||
C. | 0.36 | |||||||||||||
D. | 0.16 | |||||||||||||
17. | In a class, 15% of the students have a grade of A. Determine the probability of selecting 4 students, and none of them have a grade of A. (This problem meets all the requirements of a binomial situation.) | |||||||||||||
A. | 0.00 | |||||||||||||
B. | 0.52 | |||||||||||||
C. | 0.60 | |||||||||||||
D. | 0.85 | |||||||||||||
Suppose that the scores for this exam will follow a normal distribution with mean of 60 and a standard deviation of 15. | ||||||||||||||
18. | What is the z-score that corresponds to a test score of 85? | |||||||||||||
A. | −1.67 | |||||||||||||
B. | 1.15 | |||||||||||||
C. | 6.00 | |||||||||||||
D. | 1.67 | |||||||||||||
19. | What symmetric interval about the mean will contain approximately 95% of the test scores? | |||||||||||||
A. | 25 to 95 | |||||||||||||
B. | 15 to 105 | |||||||||||||
C. | 30 to 90 | |||||||||||||
D. | 45 to 75 | |||||||||||||
20. | What is the probability that a student's test score will be above 77? | |||||||||||||
A. | 0.13 | |||||||||||||
B. | 0.87 | |||||||||||||
C. | 0.01 | |||||||||||||
D. | 0.77 | |||||||||||||
21. | What test score falls at the 81st percentile? (rounded to the nearest whole number) | |||||||||||||
A. | 73 | |||||||||||||
B. | 81 | |||||||||||||
C. | 70 | |||||||||||||
D. | 47 | |||||||||||||
22. | What percentage of students will score between 37 and 88? | |||||||||||||
A. | 91% | |||||||||||||
B. | 97% | |||||||||||||
C. | 9% | |||||||||||||
D. | 6% | |||||||||||||
23. | Suppose random samples of 36 students are selected repeatedly from the population. What is the mean and standard deviation for the sampling distribution of sample means? | |||||||||||||
A. | Mean = 60 Standard deviation = 15 | |||||||||||||
B. | Mean = 60 Standard deviation = 2.5 | |||||||||||||
C. | Mean = 10 Standard deviation = 15 | |||||||||||||
D. | Mean = 10 Standard deviation = 2.5 | |||||||||||||
24. | What is the probability that a class composed of 36 students has a mean score less than 54? | |||||||||||||
A. | 0.9918 | |||||||||||||
B. | 0.6554 | |||||||||||||
C. | 0.0082 | |||||||||||||
D. | 0.3446 | |||||||||||||
Suppose I want to determine the average GPA of FHSU students so I randomly select 41 students and look at their GPA. Suppose that I found that those 41 students had a mean GPA of 2.40 and a population standard deviation of σ=0.8 | ||||||||||||||
25. | Compute a 99% confidence interval for the mean GPA of FHSU students. | |||||||||||||
A. | 2.40 ± 0.44 | |||||||||||||
B. | 2.40 ± 0.05 | |||||||||||||
C. | 2.40 ± 0.32 | |||||||||||||
D. | 2.40 ± 0.37 | |||||||||||||
26. | How large a sample, n, should be used to change the margin of error to 0.10 with the same 99% confidence? | |||||||||||||
A. | 468 | |||||||||||||
B. | 22 | |||||||||||||
C. | 425 | |||||||||||||
D. | 21 | |||||||||||||
27. | Consider the 99% confidence interval for the mean GPA of FHSU students. Which of the following would produce a confidence interval with a smaller margin of error? | |||||||||||||
A. | Using a confidence level of 90% | |||||||||||||
B. | Not knowing the value of σ | |||||||||||||
C. | Using a sample size of 30 students | |||||||||||||
D. | All of the above a-c | |||||||||||||
28. | Which of the following statements is true? | |||||||||||||
A. | The Central Limit Theorem states that a sampling distribution will have the same shape as the population distribution from which it is taken. | |||||||||||||
B. | The Central Limit Theorem states that the mean of a sampling distribution of means will have the same mean as the population distribution from which it is taken. | |||||||||||||
C. | The Central Limit Theorem states that the standard deviation of a sampling distribution of means will have the same standard deviation as the population distribution from which it is taken. | |||||||||||||
D. | None of a-c are true. | |||||||||||||
29. | Which of the following statements regarding confidence of population means is false? | |||||||||||||
A. | When the population is approximately normal and σ is known, use the critical value, z. | |||||||||||||
B. | When n > 30 and σ is unknown, use the critical value, t. | |||||||||||||
C. | When n < 30 and the population shape is unknown, use the critical value, z. | |||||||||||||
D. | When the population is approximately normal and σ is unknown, use the critical value t. | |||||||||||||
30. | A researcher is interested in conducting a poll on the President’s approval rating. A margin of error of at most 3% is desired. How many people must be sampled to meet this requirement at the 95% confidence level if no preliminary estimate of p-hat is known? | |||||||||||||
A. | 196 | |||||||||||||
B. | 267 | |||||||||||||
C. | 1068 | |||||||||||||
D. | 2135 | |||||||||||||
31. | The marketing director for a cereal company would like to know what proportion of households that received free samples of the cereal with their newspapers later purchase the cereal. A random sample of 207 households showed that 58 purchased the cereal after receiving the free sample. Construct a 90% confidence interval for the percentage of all households that purchased the cereal after receiving the free sample. | |||||||||||||
A. | 0.25 to 0.31 | |||||||||||||
B. | 0.20 to 0.36 | |||||||||||||
C. | 0.23 to 0.33 | |||||||||||||
D. | 0.18 to 0.38 | |||||||||||||
32. | The US census reported that it takes workers an average of 28 minutes to drive home from work. City officials in Wichita believe that it takes workers in their city less than 28 minutes to drive home from work. Which of the following gives the proper alternative hypothesis to test the claim that the average length of time for workers in Wichita to drive home from work is less than 28 minutes? | |||||||||||||
A. | H1: µ = 28 | |||||||||||||
B. | H1: µ < 28 | |||||||||||||
C. | H1: µ > 28 | |||||||||||||
D. | H1: µ ≠ 28 | |||||||||||||
33. | Suppose for a particular hypothesis test, α = 0.05 and the P-value = 0.03. Which of the following statements is false? | |||||||||||||
A. | We reject the null hypothesis. | |||||||||||||
B. | The result is statistically significant. | |||||||||||||
C. | The observed result is "unusual". | |||||||||||||
D. | The computed test statistic, z, does not fall in the shaded critical region of the tail in the normal curve | |||||||||||||
34. | It has been reported that the national average amount a single person spends annually for housing is $10,465. A random sample of 35 householders living in the Denver area had a sample mean housing cost of $12,575 and standard deviation of $4,580. Do these data indicate that householders in the Denver area spend more for housing than the national average? Compute the test statistic for this test | |||||||||||||
A. | 0.46 | |||||||||||||
B. | 2.73 | |||||||||||||
C. | 0.08 | |||||||||||||
D. | -2.73 | |||||||||||||
35. | A survey conducted five years ago showed that 79% of the households in Hays participated in the recycling program. In a recent poll of 1250 randomly selected households, 1025 said that they participate in the recycling program. A hypothesis test is to be conducted to test the claim that the population proportion of Hays households that participate in the recycling program is greater than 79%. Compute the P value for this test. | |||||||||||||
A. | 0.0029 | |||||||||||||
B. | 2.7600 | |||||||||||||
C. | 2.6000 | |||||||||||||
D. | 0.0046 | |||||||||||||
36. | The number of sales y for a company (in millions of dollars) for each year since 2005 is modeled by the equation . Use the regression equation to predict the number of sales in the year 2012 | |||||||||||||
A. | 0.6 million dollars | |||||||||||||
B. | 70.4 million dollars | |||||||||||||
C. | 16912 million dollars | |||||||||||||
D. | 238 million dollars | |||||||||||||
37. | A correlation coefficient of 0.92 between two quantitative variables A and B indicates that | |||||||||||||
A. | As A increases, B tends to increase. | |||||||||||||
B. | As A increases, B tends to decrease. | |||||||||||||
C. | Changes in A cause changes in B. | |||||||||||||
D. | There is a very weak association between A and B, and change in A will not affect B | |||||||||||||
38. | Of the scatterplot graphs below, which one represents the strongest, negative linear correlation? | |||||||||||||
A. | B. | |||||||||||||
C. | D. | |||||||||||||
A medical researcher wishes to descrive the relationship between the prescription cost of a brand name drug and its generic equivalent. The data (in dollars) are shown below. | ||||||||||||||
x (Cost of brand name drug) | 96 | 93 | 59 | 80 | 44 | 47 | 15 | 56 | ||||||
y (Cost of generic drug) | 42 | 31 | 17 | 16 | 8 | 12 | 6 | 22 | ||||||
39. | Compute the least squares regression line for the cost of generic drugs versus the cost of brand name drugs. | |||||||||||||
A. | ŷ = -4.17x + 0.382 | |||||||||||||
B. | ŷ = 0.382x - 4.17 | |||||||||||||
C. | ŷ = 0.86x + 0.74 | |||||||||||||
D. | ŷ = 0.74x + 0.86 | |||||||||||||
40. | Calculate the linear correlation coefficient between the two variables. | |||||||||||||
A. | 0.38 | |||||||||||||
B. | -4.17 | |||||||||||||
C. | 0.86 | |||||||||||||
D. | 0.74 | |||||||||||||
Ages of Hospital Patients
Frequency 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 3 3 4 4 5 7 9 8 3 2Ages
Frequency
96 93 59 80 44 47 15 56 96 93 59 80 44 47 15 56 42 31 17 16 8 12 6 22 96 93 59 80 44 47 15 56(
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