Principles of Statistics Final Exam

A pill containing no actual medicine is an example of a ______.

placebo

An experiment consists of tossing a coin and rolling a six-sided die simultaneously. Step 2 of 2: What is the probability of getting a tail on the coin and at least a 2 on the die? Round your answer to four decimal places, if necessary.

1/2*5/6=0.4167

An experiment consists of tossing a coin and rolling a six-sided die simultaneously. Step 1 of 2: What is the probability of getting a head on the coin and the number 4 on the die? Round your answer to four decimal places, if necessary.

1/2⋅1/6=1/12≈ 0.0833

An experiment consists of tossing a coin and rolling a six-sided die simultaneously. Step 2 of 2: What is the probability of getting a tail on the coin and at least a 5 on the die? Round your answer to four decimal places, if necessary.

1/2⋅2/6≈ 0.1667

Identify the population being studied. The overall exam scores of 14 out of the 37 students in your statistics class.

All the students in your statistics class.

Consider the following sets of sample data: A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312 B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41 Step 2 of 2: Which of the above sets of sample data has the larger spread?

Answer:Data Set B

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1140 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 80 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1089.64 milligrams of sodium per package with a sample standard deviation of248.67 milligrams. Step 2 of 2: Using the confidence interval approach, is there evidence that the sodium content is different from what the nutrition label states?

Because the hypothesized value falls in the interval, we fail to reject the null hypothesis. There is not sufficient evidence at the 99% confidence level that the sodium content is different from what the nutrition label states.

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 16 samples is 4.4 ppm with a variance of 0.64. Assume the population is normally distributed. Does the data support the researcher's claim at the 0.05 level? Make the decision to reject or fail to reject the null hypothesis.

Comparing the P-value we calculated to the level of significance, we see that 0.0455≤0.05, so we will make the decision to reject the null hypothesis. Correct Answer: Reject Null Hypothesis

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 21 bag sample had a mean of 401 grams with a standard deviation of 26. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Correct Answer: Reject H0 if t<−1.325 10% t-Lower Critical in RGuroo

In order to help decide when and where to advertise, an electronics repair company decided to pull invoices and tally what types of devices were repaired. There were twenty-five devices repaired that month. What is the level of measurement for the data? Are the data qualitative or quantitative? Electronics Repaired LaptopTabletPrinterLaptopFaxLaptopTabletFaxCell PhoneLaptopCell PhoneFaxCell PhoneFaxCell PhoneTabletLaptopCell PhoneTabletFaxCell PhonePrinterFaxPrinterCell Phone

Correct Answer: nominal, qualitative

For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning. The price of cars on a car lot

Correct measure of center: Median Justification: The prices of the cars are quantitative data with outliers

Consider the following data: x −4 −3 −2 −1 0 P(X=x)0.3 0.1 0.1 0.2 0.3 Step 3 of 5: Find the standard deviation. Round your answer to one decimal place.

Descriptive Statistics >Two Variable TI 84 See input instructions. Answer: 1.6

Consider the following data: x −4 −3 −2 −1 0 P(X=x)0.3 0.1 0.1 0.2 0.3 Step 2 of 5: Find the variance. Round your answer to one decimal place.

Descriptive Statistics >Two Variable TI 84 See input instructions. use standard deviation and square Answer: 2.4

Determine whether the statement describes a descriptive or inferential statistic. 65% of all students at the local university voted in the last election.

Descriptive statistic.

Classify the following as either a discrete random variable or a continuous random variable. The populations of countries that belong to the United Nations.

Discrete

The numbers of people in each statistics class at your school are an example of which type of data?

Discrete

Determine whether an observational or experimental study is appropriate to address the following statement. A deli cart entrepreneur wants to find out if dressing an employee in a gorilla costume will bring in more customers.

Experimental

Determine whether an observational or experimental study is appropriate to address the following statement. A gas station owner wants to study if closing the store early on weeknights will hurt profits.

Experimental

Decide if the following statement is true or false. It is possible to have a variance of −20 for some data set.

False

Write out the sample space for the given experiment. Use the letter H to indicate heads and T for tails. 3 coins are tossed.

HHH,HHT,HTH,HTT,THH,THT,TTH,TTT

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 30 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The 11th percentile of the data is 15 hours. Step 3 of 5: Based on the given information, determine if the following statement is true or false. Approximately 109 families turned on their televisions for less than 26.2 hours.

In the survey, there are approximately 218 families. So, approximately 109 families represent 50% of the data. The median is the 50th percentile which splits the data into two groups of approximately 109 families. The problem states that the median is 26.2. Thus, a total of 109 families turned on their televisions for less than 26.2 hours and hence, the given statement is true.

Religious affiliations are an example of which type of data?

Neither Continuous or Discrete

Songs on a band's set list are an example of which type of data?

Neither Continuous or Discrete

Determine whether an observational or experimental study is appropriate to address the following statement. A deli cart entrepreneur wants to find out if her customer base is shrinking.

Observational

Determine whether the statement describes a population or a sample. The overall exam scores in your math class.

Population

Determine if the numerical value describes a population parameter or a sample statistic. 68% of all instructors at your school teach 2 or more classes.

Population Parameter

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. Fifty people were asked to respond to a survey question regarding how frequently they used their credit card. The categories they were asked to choose from are given below: 1) Infrequently 2) Sometimes 3) Frequently

Qualitative Neither Ordinal

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. Five people are in a bakery waiting for service. Each person takes a ticket when they enter the bakery in order to determine when they will be served. The person with the lowest ticket number will be served next.

Qualitative Neither Ordinal

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. The total weight of sugar imported by the United States each day for a year.

Quantitative Continuous Ratio

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. The IQ scores of students at the local college.

Quantitative Discrete Interval

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. The prices of 50 randomly selected cars.

Quantitative Discrete Ratio

An experiment consists of tossing a coin and rolling a six-sided die simultaneously. Step 1 of 2: What is the probability of getting a head on the coin and the number 5 on the die? Round your answer to four decimal places, if necessary.

1/2*1/6=0.0833

Fill in the blank with the most appropriate term. Factors that influence the results of a study that the researcher did not, or could not, account for are known as ______?

Confounding Variables

Classify the following as either a discrete random variable or a continuous random variable. The temperature in Kelvin on the planet Jupiter.

Continuous

Lengths of time it takes for new light bulbs to burn out are an example of which type of data?

Continuous

Widths of the doors in a restaurant are an example of which type of data?

Continuous

A reviewer decides to interview patrons to see how they would rate a particular restaurant. The following table lists the responses from twenty-five patrons. What is the level of measurement for the data? Are the data qualitative or quantitative? Restaurant RatingsFive StarsOne StarTwo StarsThree StarsFour StarsThree StarsFour StarsFour StarsFive StarsThree StarsFive StarsFour StarsThree StarsFour StarsFive StarsOne StarThree StarsFive StarsOne StarTwo StarsFive StarsTwo StarsFour StarsOne StarFive Stars

Correct Answer: ordinal, qualitative

Consider the following data: x −4 −3 −2 −1 0 P(X=x)0.3 0.1 0.1 0.2 0.3 Step 1 of 5: Find the expected value E(X)E(X). Round your answer to one decimal place.

Descriptive Statistics >Two Variable TI 84 See input instructions Answer: -1.9

The numbers of each color of jelly beans in a jar (assuming they are all whole) are an example of which type of data?

Discrete

Determine whether the statement describes a descriptive or inferential statistic. A recent poll of 2935 luxury car owners in West Virginia showed that the average price of a luxury car in the U.S. is $27,100.

Inferential Statistic

Determine whether the statement describes a descriptive or inferential statistic. A recent poll of 3355 students in Michigan showed that the average number of hours a U.S. college student studies per week is 9.7.

Inferential Statistic

12,13,15,8,2,4 Determine the mean of the given data.

Mean=12+13+15+8+2+4/6 = 9

Determine whether an observational or experimental study is appropriate to address the following statement. A gas station owner wants to study if a need for additional staffing exists.

Observational

Consider the following data: x −4 −3 −2 −1 0 P(X=x)0.3 0.1 0.1 0.2 0.3 Step 4 of 5: Find the value of PP(X≥−1). Round your answer to one decimal place.

P(X≥−1)= P(X=−1)+P(X=0) = 0.2+0.3 = 0.5

63% of all freshmen at your school reside on campus.

Population Parameter

Identify the population being studied and the sample chosen. The final exam scores of 4 out of the 27 students in your psychology class.

Population: All the students in your psychology class. Sample: 4 out of the 27 students in your psychology class.

Types of cars people own are an example of which type of data?

Qualitative

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. A business must keep a record of each employee's social security number.

Qualitative Neither Nominal

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. Survey responses to the question "What is the gender of your first child?" 1) Male 2) Female

Qualitative Neither Nominal

Heights of sunflowers in a garden are an example of which type of data?

Quantitative

Pounds gained by persons in your class during the first month of the semester are an example of which type of data?

Quantitative

Consider the following sets of sample data: A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312 B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41 Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

The CV is the ratio of the standard deviation to the mean as a percentage. The mean of Data Set A is x‾=359.8 and the sample standard deviation is s=60.9. A: 60.9/359.8⋅100%≈16.9%. Answer: 16.9%. the mean of Data Set B is x‾=1.791and the sample standard deviation is s=0.635. B: 0.635/1.791⋅100%≈35.5%. Answer: 35.5%

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 3030 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 1515 hours or less for the week. The 11th percentile of the data is 1515 hours. Step 4 of 5: What is the value of the 50th percentile?

The median is the 50th percentile so, 26.2

Suppose that a Senate committee is composed of 15 Senators of whom 4 are left-handed. What proportion of the committee are left-handed? Either give the exact fraction or decimal, or round to three decimal places.

There are 15 people on the committee, N=15. The number of people on the committee who are left-handed is 4, X=4. Therefore, the proportion of the committee who are left-handed is p=X/N=4/15≈0.267.

A regional Internet provider keeps records of complaints received from its customers. Complaints for last month are listed in the following table. What percent of the complaints are due to the categories Long customer service wait times or Unreliable/Frequently stops working? Round your answer to two decimal places, if necessary. Type of ComplaintFrequency Too expensive174 Unreliable/Frequently stops working242 Page loading too slow111 Download/Upload speed too slow98 Extra data usage charges67 Poor tech support103 Long customer service wait times59 Incorrect billing46 Long wait for installation75

To calculate the percent of complaints for the categories Long customer service wait times or Unreliable/Frequently stops working, first sum all the frequencies in the table to get the total number of complaints, 975. Then sum the frequencies for the categories Long customer service wait times and Unreliable/Frequently stops working and divide by 975. Multiply this result by 1100 to convert to a percent. The percent of complaints for the categories Long customer service wait times or Unreliable/Frequently stops working would then be computed as follows: 59+242/975⋅100%=301/975⋅100≈30.87 Correct Answer: 30.87%

A small commuter airline keeps records of complaints received from its customers. Complaints for last month are listed in the following table. What percent of the complaints are due to the category Airplane too cold? Round your answer to two decimal places, if necessary. Type of ComplaintFrequency Tickets cost too much26 Stewardess did not provide blankets44 Schedules not convenient29 Plane often late33 Seats too stiff66 Airplane too hot21 Airplane too cold14 Poor reservation system10 Plane interior looks shabby8

To calculate the percent of complaints for the category Airplane too cold, first sum all the frequencies in the table to get the total number of complaints, 151. Then divide the frequency for the category Airplane too cold, 14, by 151. Multiply this result by 100 to convert to a percent. The percent of complaints for the category Airplane too cold would then be computed as follows. 14/151⋅100%≈9.27 Answer: 9.27%

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≤1), n=5, p=0.4

RGuroo -> Probability-Simulation -> Probability Calculator -> Discrete -> Values ⇒ Probability Enter data and Graph Answer: 0.337

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X<3), n=4, p=0.6

RGuroo -> Probability-Simulation -> Probability Calculator -> Discrete -> Values ⇒ Probability Enter data and Graph Answer: 0.5248

Determine whether the statement describes a population or a sample. The annual salaries of a sample of 2626 parents of your classmates.

Sample

Determine if the numerical value describes a parameter or a statistic. A recent poll of 2707 home owners in Michigan showed that the average price of their houses is $⁢265,000.

Sample Statistic

Determine if the numerical value describes a parameter or a statistic. A recent poll of 2940 corporate executives showed that the average price of their cars is $⁢31,800.

Sample Statistic

Determine if the numerical value describes a parameter or a statistic. A survey of 3740 people in the U.S. revealed that 76% of those surveyed work a full-time job.

Sample Statistic

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 3030 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The 11th percentile of the data is 15 hours. Step 5 of 5: Based on the given information, determine if the following statement is true or false. The first quartile is less than 15 hours.

The 11th percentile of the data is 15 hours. The first quartile is the 25th percentile. Since 25th percentile ≥ 11th percentile, First quartile ≥15 hours. Thus, the first quartile is greater than or equal to 15 hours and hence, the given statement is false.

A chemist examines 15 geological samples for potassium chloride concentration. The mean potassium chloride concentration for the sample data is 0.376 cc/cubic meter with a standard deviation of 0.0012. Determine the 95% confidence interval for the population mean potassium chloride concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

The correct value for tα/2 is 2.145.

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 30 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The 11th percentile of the data is 15 hours. Step 1 of 5: Based on the given information, determine if the following statement is true or false. The 54th percentile is greater than or equal to 25 hours.

The median is the 50th percentile. And the problem states that the median is 26.2 hours. Since 54th percentile ≥ 50th percentile (by the definition of a percentile), 54th percentile ≥26.2. It is clear that the 54th percentile is greater than or equal to 26.2 hours and hence the given statement is true.

12,13,15,8,2,4 Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.

The mode is the value in the data set that occurs most frequently. - No Mode

A sample of 280 registered voters in a state were asked which party's candidate they planned to vote for in an upcoming election. 116116 of those surveyed said that they planned to vote for the Democratic candidate. Calculate the sample proportion of voters who planned to vote for the Democratic candidate. Either give the exact fraction or decimal, or round to three decimal places.

There are 280 voters in the sample, n=280. The number of voters in the sample who planned to vote for the Democratic candidate is 116, X=116. Therefore, the sample proportion of voters who planned to vote for the Democratic candidate is pˆ=X/n= 116/280= 29/70 ≈ 0.414

A regional Internet provider keeps records of complaints received from its customers. Complaints for last month are listed in the following table. What percent of the complaints are due to the category Long wait for installation? Round your answer to two decimal places, if necessary. Type of ComplaintFrequency Too expensive174 Unreliable/Frequently stops working242 Page loading too slow111 Download/Upload speed too slow98 Extra data usage charges67 Poor tech support103 Long customer service wait times59 Incorrect billing46 Long wait for installation75

To calculate the percent of complaints for the category Long wait for installation, first sum all the frequencies in the table to get the total number of complaints. Then divide the frequency for the category Long wait for installation by the total. Don't forget to multiply this result by 1100 to convert to a percent and round your result to two decimal places. 75/975*100=7.69%

A regional Internet provider keeps records of complaints received from its customers. Complaints for last month are listed in the following table. What percent of the complaints are due to the category Page loading too slow? Round your answer to two decimal places, if necessary. Type of ComplaintFrequency Too expensive174 174Unreliable/Frequently stops working242 242Page loading too slow111 111Download/Upload speed too slow98 98Extra data usage charges67 67Poor tech support103 103Long customer service wait times59 Incorrect billing46 46Long wait for installation75

To calculate the percent of complaints for the category Page loading too slow, first sum all the frequencies in the table to get the total number of complaints. Then divide the frequency for the category Page loading too slow by the total. Don't forget to multiply this result by 100100 to convert to a percent and round your result to two decimal places. 111/975*100=11.38%

The number of burglaries in a city is depicted in two different graphs below. How many times more burglaries were there actually in Year 4 compared to Year 1? Round your answer to 2 decimal places.

To find how many times more burglaries there were in Year 4 compared with Year 1, divide the number of burglaries in Year 4 by the number of burglaries in Year 1. There are 260 burglaries in Year 4 and 225 burglaries in Year 1. Thus, the answer, rounded to 2 decimal places, is 260/225≈1.16. Correct Answer: 1.16

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1140 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 80 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1089.64 milligrams of sodium per package with a sample standard deviation of 248.67 milligrams. Step 1 of 2: Calculate a 99% confidence interval for the mean sodium content in Oriental Spice Sauce.

Use T test (1016.24,1163.04)

Calculate the interquartile range of the given data. 24,6,35,20,26,46,21,39,51,6,38,32,15,30,22

place the data in ascending order. 6,6,15,20,21,22,24,26,30,32,35,38,39,46,51 find the location of the 75th percentile in the ordered data. 15(75/100)=11.25 Since the location is a decimal value, we will round up to the next greatest integer, 12, and the 75th percentile value will be in the 12th position of the ordered data. Therefore, Q3=38 find the location of the 25th percentile in the ordered data. 15(25/100)=3.75 Since the location is a decimal value, we will round up to the next greatest integer, 4, and the 25th percentile value will be in the 4th position of the ordered data. Thus, Q1=20 Therefore, the interquartile range of the data is 38−20=18

If the nurses administering care know which participants received a placebo or treatment, but the participant does not have this information, the experiment is _____.

single-blind

If the researchers administering care know which partakers have been placed in the experimental or control group, but the partaker does not have this information, the experiment is _____.

single-blind

In a ____ experiment, only the subject does not know whether they have been placed in the control or experimental group.

single-blind

Identify the sample chosen for the study. The types of cars of a sample of 24 employees at the local news network.

the 24 employees at the local news network.

The _____ receives an active drug while the other group does not.

treatment group

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 30 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The 11th percentile of the data is 15 hours. Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.

x=number of data values less than or equal to x divided by the total number of data values⋅100 Therefore, x=15 hours, percentile of 15 hours =11, and number of data values less than or equal to 15 hours =24. 24/11⋅100≈218.