Statistical Analysis in Social Sciences and Business
Probability Calculation with Defective Items
A sample of 4 calculators was extracted from a total order, of which 36 are defective and 28 are not. What is the probability that the four selected calculators are defective?
a) 0.1001
Hypothesis Testing: Americans Sharing Homework Responsibilities
An article in a sociology journal states that at least 66% of Americans share responsibility with their spouses to monitor their children’s homework. In a city in California, a study was conducted involving a random sample of 234 parents. It was found that 138 said they share this responsibility with their spouses. A significance level of 0.05 was used to perform a test using Statdisk, and the following results were obtained:
- Test statistic: -2.2687
- Critical value: -1.6449
- P-value: 0.0116
Which of the following hypothesis tests allows for the assertion of the article?
D) H0: p = 0.66, H1: p < 0.66
Correlation: College Entrance Exam Scores and GPA
A random group of 20 students who completed their first year in college had their entrance exam scores and first-year grade point averages recorded. The correlation coefficient is significant. Which of the following statements is a correct interpretation of the correlation coefficient?
- The relationship between the variables is straightforward.
- A higher score for admission is expected to result in a higher GPA during the first year.
- A higher score for admission would be expected to result in a lower GPA during the first year.
E) I and II
Box Plots: Comparing Car Mileage
Tests were conducted to determine the mileage per liter of three different cars. The results were presented with the following box plots:
Which of the following statements are correct regarding the values of mileage per gallon?
- The three cars have the same interquartile range.
- Car B has an approximately symmetrical distribution.
- Car B has a smaller range.
E) Only II
Hypothesis Testing: Washing Machine Lifespan
A washing machine manufacturer states that the average useful life… A random sample of 50 washers… 2.1 years. If you want to compare… which of the following hypotheses represent the null and alternative hypotheses?
A) H0: μ = 7.1, H1: μ < 7.1
Sales Data Distribution Shape
Sales in thousands of dollars made by a group of sellers last month were summarized in the following descriptive measures. According to the results in the table, what would be the shape of the distribution of sales values of these workers? (Statdisk) Mean: 21.3906
A) Symmetrical, B) Skewed left, C) Skewed right, D) Cannot be determined
Confidence Interval: Students Acquiring Textbooks
The manager of the university library wants to estimate the percentage of students who acquire textbooks for the statistics class. He has taken a random sample of 600 students and found that 320 of them bought the textbook for that class.
A confidence level of 95% obtained a range for the actual proportion of students going from 0.493 to 0.573. What would be the most appropriate interpretation for this result?
A) We can say with 95% certainty that the actual percentage of students who purchase textbooks for the statistics class is contained in the range going from 49.3% to 57.3%.
Study Type: Divorce Rate Analysis
A sociologist wants to determine the annual rate of divorces in a given city. He plans to analyze the records from 1950 to the present regarding the divorce rate. The type of study that describes this statement is:
A) Experimental, B) Observational retrospective, C) Cross-sectional, D) Observational prospective
Confidence Interval: Time Spent on Math Tasks
A random sample of 150 students was selected, and they were asked how much time they devote weekly to performing tasks in a mathematics course. A 98% confidence interval for the population mean was obtained. The range is from 5.2 to 8.3 hours. What would be the most appropriate interpretation of this result?
A) There is a 98% certainty that the average time the student population of the mathematics class devotes to the accomplishment of tasks is contained in the interval ranging from 5.2 to 8.3 hours a week.
Defective Products: Parameter or Statistic?
A manufacturer claims that only 5% of the products it manufactures are defective. This statement describes a:
A) Variable, B) Data point, C) Parameter, D) Statistic
Rare Occurrence Rule: Identifying Unusual Events
According to the rule of rare occurrences, which of the following probability values should be associated with a rare or unusual event?
- P(A) = 0.018
- P(A) = 0.0078
- P(A) = 0.078
B) I and II
Confidence Interval: Public Transportation Attitude Test
A sociologist has developed and validated a test to measure attitudes toward the use of public transportation. In the validation process, it has been found that the distribution of scores for this test follows a bell-shaped distribution. 27 adults were selected at random from a small community, and they took the test. The average of this group of adults was 76.2, with a standard deviation of 21.4. Construct a 95% confidence interval for the average score on this test for the population from which these adults were selected.
b) 74.6 < μ < 77.8
Hypothesis Testing: Americans and Homework Supervision
An article in a sociology journal states that at least 66% of American parents share the responsibility of supervising their children’s homework with their spouses. In a city in California, a study was conducted involving a random sample of 234 parents. It was found that 138 said they share this responsibility with their spouses. A significance level of 0.05 was used to conduct a test using STATDISK, and the following results were obtained:
- Test statistic: -2.2687
- Critical value: -1.6449
- P-value: 0.0116
C) The sample provides significant evidence to conclude that the assertion of the article is false. Therefore, we can say that less than 66% of American parents share responsibility with their spouses for supervising their children’s homework.
Garden Size Distribution
A nursery has collected data for a group of sectors in a city, specifically the area in square meters of front gardens that use some type of grass.
| Dimensions (in m2) | Number of Houses |
|---|---|
| 0 to 14 | 2 |
| 15 to 19 | 12 |
| 20 to 24 | 20 |
| 25 to 29 | 21 |
| 30 to 34 | 13 |
| 35 to 39 | 2 |
What is the percentage of housing that has a garden with an examined area of at least 25 square meters?
D) 51.43%
Unusually High Income Threshold
It is known that the monthly income of some employees has an average of $5300 with a standard deviation of $450. What are the parameter limits that might be considered to mean that income is unusually high?
B) $6200 (5300 + 2 x 450)
Textbook Purchase: Statistic or Parameter?
In a random sample of 500 students, it was found that 45% of them buy their textbooks. The above statement describes a:
A) Statistic
Service Time Consistency at Fast Food Restaurants
The time required to service a car at two fast-food restaurants has been summarized in the following descriptive measures:
| Restaurant A | Restaurant B | |
|---|---|---|
| Average | 186.3 | 262.5 |
| Median | 184 | 262.5 |
| Variance | 4081.7 | 16644.3 |
| Range | 195 | 407 |
| Minimum | 92 | 74 |
| Maximum | 287 | 481 |
| n | 60 | 60 |
Which of the following restaurants will have greater consistency in the time to service a car?
A) Restaurant A
Confidence Interval: Time Spent Watching TV
A researcher wants to estimate, for a particular school district, the average time per week that 6th-grade children spend watching television. She took a random sample of 25 students and asked them for the hours they spend watching television. She found that the mean of this group of students was 10.5 hours per week. She knows from previous studies that the population standard deviation is 4.0 hours and that, under these conditions, the distribution is skewed to the left. For a 99% confidence interval for the average time per week that 6th-grade students in said district spend watching television, she should use:
B) Neither the t-distribution nor the Z-distribution. Other estimation methods must be sought.
Stopping Distance: Variable Type
The distance traveled before stopping a car once the brakes are applied is an example of a:
A) Quantitative continuous variable
Probability of Observing a Higher Mean
It is known that the monthly income of workers in a certain locality is normally distributed with a mean of $3500 and a standard deviation of $30. If a researcher has chosen a random sample of 25 men and wants to determine the probability of observing a mean higher than $4000, in which situation is the investigator?
C) The normal distribution can be used because the population standard deviation is known, and the population has a bell-shaped distribution.
Canned Product Weight: Variable Type
The weight of a canned product illustrates a:
C) Quantitative continuous variable
Hypothesis Testing: Car Mileage Claim
The Carter Motor Company says its new sedan, Libra, has an average output beyond 23 miles per gallon in the city. In which of the following options are the null and alternative hypotheses rendered to test the claim of the company?
C) H0: μ = 23, H1: μ > 23
Confidence Interval: Students Purchasing Textbooks
The manager of the university library wants to estimate the percentage of students who purchase textbooks for the statistics class. He has taken a random sample of 600 students and asked them if they purchased this textbook for the statistics class. Of the total respondents, 320 of them bought the textbook for that class.
If a 90% confidence interval is desired for the actual proportion of students, one should use:
D) Cannot be determined which distribution to use due to lack of information
Study Type: Vacation Plans
A market researcher wants to determine the percentage of citizens who plan to go on vacation this year. The type of study that describes this statement is:
B) Cross-sectional
Rejected Coin Rate
It is known that the weights of 25-cent coins are normally distributed with a mean of 5.67g and a standard deviation of 0.07g. A vending machine accepts coins of this denomination whose weights are between 5.48g and 5.82g. What is the rate of 25-cent legal tender that would be rejected?
C) 1.96%
Study Type: Voter Turnout
A sociologist wants to determine the percentage of citizens who went to vote in the elections for governor held last year in a state. The type of study described by this statement is:
B) Observational cross-sectional
Sampling Method: Opinion Poll on Drunk Driving Penalties
A researcher is conducting an opinion poll regarding tougher penalties for drunk driving. They decide to poll at different points of greater affluence and interview adults who pass through there during the days they have decided to visit those places. The above statement is describing:
Conglomerate sampling
Margin of Error Calculation
To determine the proportion of students who buy the textbook for the statistics class, a random sample of students was used, and the confidence interval was determined to be:
0.842 < p < 0.880
Based on this information, what would be the margin of error, E?
A) 0.019
Washing Machine Replacement Time
Replacement times for washing machines are normally distributed with a mean of 10.8 years and a standard deviation of 1.2 years. What is the replacement time such that 87% of washing machines are below that value?
C) 11.9 years