Unit One - Categorical Variables

Which of the following can be reasonably modeled by a normal distribution? The favorite colors of students in a kindergarten class The heights of tomato plants that were all planted on the same day The percent of employees from a company who attended a company retreat The average number of siblings of all students at a particular high school The parental guidance ratings (GG, PGPG, PG-13PG-13, RR) of movies filmed in 2019

The heights of tomato plants that were all planted the same day

If the size of the intervals/bind of a histogram were decreased, what must remain the same on the new histogram? The heights of the bars The widths of the bars The number of bars The sum of the frequencies The shape of the distribution

The sum of the frequencies

A local ice-cream shop sells ice-cream cones for $2.00, and customers can choose from the following options. Ice-cream flavor Type of cone: sugar or waffle Chocolate dipped for an additional $0.50 Sprinkles for an additional $0.50 Which of the following is a quantitative variable? Ice-cream flavor Type of cone Chocolate dipped or not Sprinkles or not The total cost of the cone

The total cost of the cone

Data were collected on 100 United States coins minted in 2018. Which of the following represents a quantitative variable for the data collected? The type of metal used in the coin The value of the coin The color of the coin The person depicted on the face of the coin The location where the coin was minted

The value of the coin

Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data? How many blue cars are in the lot? What are the gas mileages, in miles per gallon, of the cars in the lot? What are the weights, in pounds, of the cars in the lot? What is the number of cars in the lot with out-of-state license plates? What are the colors of the cars in the lot?

What are the colors of the cars in the lot

A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco weighs 8 pounds. A cat's weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the following is the best description of Gordo's and Flaco's weights? Neither Gordo's nor Flaco's weight is classified as unhealthy. Gordo's weight is classified as unhealthy but Flaco's weight is not. Flaco's weight is classified as unhealthy but Gordo's weight is not. Flaco's weight and Gordo's weight are both classified as unhealthy. The classification of weight cannot be determined without more information.

Gordo's weight is classified as unhealthy but Flaco's weight is not.

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported? I The median is not likely to change. IIThe range is not likely to change. III The mean is likely to increase. II only III only II and IIII only II and IIIIII only II, IIII, and III

II and III only

Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. Is Roger's claim correct? Yes, both the mean and median are likely to change greatly. No, only the mean is likely to change greatly. No, only the median is likely to change greatly. No, neither the mean nor the median are likely to change greatly. There is not enough information to determine if the mean or the median is likely to change greatly.

No, only the mean is likely to change greatly

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58 One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim? Yes, there are two outliers. One outlier is 9 minutes and the other outlier is 58 minutes. No, there is only one outlier at 9 minutes. No, there is only one outlier at 58 minutes. No, there are three outliers. One outlier is 9 minutes, one outlier is 35 minutes, and one outlier is 58 minutes. No, there are no outliers.

No, there is only one outlier at 58 minutes.

True or False: Medians are resistant to outliers

True

The distribution of the amount of a customer's purchase at a convenience store is approximately normal, with mean $15.50 and standard deviation $1.72. Which of the following is closest to the proportion of customer purchase amounts between $14.00 and $16.00 ? 0.19 0.39 0.42 0.61 0.81

0.42

The distribution of the number of transactions performed at a bank each day is approximately normal with mean 478 transactions and standard deviation 64 transactions. Which of the following is closest to the proportion of daily transactions greater than 350 ? 0.023 0.046 0.477 0.954 0.977

0.977

In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all daily high temperatures are between 83°F and 89°F. What is the standard deviation of the distribution? 1°F1°F 1.5°F1.5°F 2°F2°F 3°F3°F 6°F6°F

1.5 (89-83)/4= 1.5

A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine? 19.3mm 20.6mm 22.1mm 23.5mm 24.9mm

20.6 mm

Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR rule for outliers, is there evidence to support the claim? Yes, because (max−Q3)(max⁡−Q3) is greater than (Q1−min)(Q1−min). Yes, because 43 is greater than (Q3 +IQR) Yes, because 43 is greater than (Q1−1.5×IQR) No, because 43 is not greater than (Q3+1.5×IQR) No, because 43 is greater than (Q1−1.5×IQR)

No, because 43 is not greater than Q3+1.5 x IQR)

Data are collected on the 35 students in a college history course. Which of the following is not a variable for the data set? Student birth month Political affiliation of student Student age Student address Number of students in the data set

Number of students in the data set

What is the formula of an outlier?

Q1 -1.5 x IQR Q3+1.5 x IQR

The following list shows the number of video games sold at a game store each day for one week. 15, 43, 50, 39, 22, 16, 20 Which of the following is the best classification of the data in the list? Categorical and continuous Quantitative and continuous Categorical and discrete Quantitative and discrete Neither categorical nor quantitative, and neither discrete nor continuous

Quantitative and discrete

Which of the following describes a continuous variable? The number of items sold at a craft booth for one day The number of apps downloaded from a website one day The diameters of the tree trunks at an evergreen farm The number of baskets made by a basketball player The shoe sizes of all shoes on sale at a department store

The diameters of the tree trunks at evergreen farm

Which of the following statements is true about a distribution that appears to have a gap when displayed as a histogram? The distribution must have an outlier. The distribution has a region between two data values where no data were observed. The distribution is approximately normal. The distribution cannot be symmetric. The distribution must be bimodal.

The distribution has a region between two data values where no data were observed

When a distribution is skewed to the left, what is the relationship between the mean and median? The mean and median are equal in value The mean is less than the median The mean is greater than the median

The mean is less than the median

Data will be collected on the following variables. Which variable can be considered discrete? The height of a person The weight of a person The length of a person's arm span The time it takes for a person to solve a puzzle The number of books a person finished reading last month

The number of books a person finished reading last month

At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution? There were 770 entries with a score less than or equal to 68. There were at least 230 entries with a score of 77. There were 23% of the entries with a score less than or equal to 68. There were 77% of the entries with a score equal to 68. There were at least 77% of the entries with a score greater than 68.

There were 770 entries with a score less than or equal to 68

The distribution of the number of moths captured per night by a certain moth trap is approximately normal with mean 103. If 28 percent of the captures fall below 76 per night, which of the following equations can be used to find σ, the standard deviation of the distribution? 0.28=103−76/σ 0.28=76−103/σ −0.58=103−76/σ −0.58=76−103/σ 0.58=76−103/σ

−0.58=76−103/σ