CISB 241 Midterm
A radio ad states that the mean (average) waiting time for a pizza is less than 20 minutes. You want to set up a hypothesis to test this claim. The claim -- less than 20 minutes -- is represented by the _____________ hypothesis.
Alternative
Find the probability associated with a z-value = -0.93.
0.3238
The average grade on a statistic midterm is 88 points out of 100 (just an example). The standard deviation of grades on the midterm is 9 points. If a student receives a 92 on the midterm, what is her score when converted to a z-value?
0.44
Find the probability associated with a z-value = 1.87.
0.4693
The following is an appropriate statement of the null and alternate hypotheses for a test of a population mean: H0 : μ < 50 HA : μ > 50
False
The police chief in a local city claims that the average speed for cars and trucks on a stretch of road near a school is at least 45 mph. If this claim is to be tested, the null and alternative hypotheses are: H0 : μ < 45 mph Ha : μ ≥ 45 mph
False
Variance measures the average of a population or sample.
False
What is a pilot sample? It is a sample of observations used to find the sample standard deviation in problems when you are tying to find the necessary sample size and the population standard deviation is unknown after you actually select the necessary sample size.
False
Two classes of random variables exist: Discrete and Noncontiguous
False Discrete and Continuous
In hypothesis testing, three hypotheses are formed, the null, alternative, and subsidiary.
False, Only two: null and alternative
The definition of a One-tailed Test - a test in which the null hypothesis can be rejected if the sample mean is inconsistent with the hypothesized population mean - either larger or smaller (H0:µ = 0)
False, this is the definition of a two-tailed test
If your sample size gets larger and larger, what happens to its ability to better represent the population from which it is drawn from?
Gets better
What does frequency show?
How many times an observation in a dataset occurs.
In the relative frequency table below, which of the following is nota true statement?
In this sample, 65% of all vehicles owned are sports cars, 35% are SUVs
This week, we are studying discrete and continuous random variables. The following characterize a continuous random variable except...
Is determined by counting
From an analyst's perspective, how can this useless table below be turned into useful information?
It can be turned into a frequency table
Which of the following does not define the margin of error?
It is the same as sampling error
Which of the following is an example of a leading question?
Like most smart people, do you support tax breaks for those buying electric vehicles?
Why are presentations and reports of your data important?
They effectively transform data into information.
When a battery company claims that their batteries last longer than 100 hours and a consumer group wants to test this claim, the hypotheses should be: H0 : μ ≤ 100 HA : μ > 100
True
When finding the probability of a z-value in the standard normal table, the probability found is between the z-value and the mean, 0.
True
When you use the Standard Normal Distribution Table (Appendix D, page 764) to find probabilities associated with z-values, the probability you get from the table is between the mean of the normal curve, 0, and the z-value (even if your z-value is negative).
True
The standardized normal z-value scales any normal distribution axis from its true units (time, weight, dollars, etc.) to the standard measure referred to as its z-value.
True See page 215
In hypothesis testing, we make a hypothesis (or statement) concerning a population parameter, we then use sample data to either deny or confirm the validity of the proposed hypothesis.
True, See page 316
Which of the following is NOT a questioned asked of business decision-makers when thinking about what size of sample is needed?
What questions do you want to add to your survey?
If I take a random sample of football players. Let's say 10 out of 100 players. And then I take another random sample of 10 without putting the first 10 back into the population, then this is sampling....
Without replacement
What is a population proportion?
The population percentage of interest within the broader population
A marketing company surveyed 20 consumers to see whether they prefer online or in-store shopping. Prior surveys revealed that 65% of consumers prefer in-store shopping. Assuming the 65% is correct, what is the probability that in a randomly selected sample of 20 people, 14 or fewer would prefer in-store shopping? To help with the problem: Define p and q; Define your n (sample size); Define your x, event of interest (Hint: Follow the example on page 186, Example 5-4, use the Excel formula on page 186 and 187 to find the binomial distribution probability where numbers_s = x (event of interest) and trials = sample size).
0.75
The population proportion is 30 of Americans that love chocolate ice cream (I mean, really love). The sample proportion of Americans that say they love chocolate ice cream is 40, then the sampling error is...
10
In the following table, what is the joint probability that a randomly selected kid is a boy and a cat lover?
18%
When using the Normal Distribution to find probability of a continuous random variable, the probability returned to you is between your variable of interest and negative infinite. In order to find the probability above your variable of interest, you need to take 1 - (minus) your resulting probability. This is because the probability under the standard normal curve is equal to 1.0 and the probabilities calculated are cumulative. Take an example. The mean apple weight is 8 oz. with a standard deviation of 0.5 oz. What is the probability that a randomly selected apple will have a weight of 9 oz. or heavier? That is, P(x ≥ 9) = ?? Hint: Page 217 Business Application, but, use the NORM.DIST formula on the top of page 217, not the STANDARDIZE formula
2% probability that a randomly selected apple will weight 9 oz. or heavie
If there are 100 people in your population (you are on a very small island) and you know that 20 do not like coconut in your population, then what is the population proportion that do not like coconut?
20/100
I love to hike, I hike an average 8 miles per day (not really). Within that distance, I like about 2 miles of steep incline, 1 mile of going downhill, and 5 miles of flat. What is the probability that if I pick any mile within in this 8 miles that it will be a steep incline?
25%
In the below table, what is the conditional probability that a student gets a tutor 2 to 3 times given that the student is a part-time student?
38%
In the following table, what is the probability that a randomly selected kid (girl or boy) is a dog owner?
44%
If mean = 3, standard deviation = 0.25, what is P(2 ≤ x ≤ 8) =?? Use Example 6-2 and NORM.DIST formula at the bottom of page 219 for hint.
48%
What is the range of the following data? 1, 2, 3, 4, 5, 6
5
Fill in the blank. According to the textbook, the amount of data available is growing at a rate of ______ percent per year.
50
In the histogram below, which age group has the highest frequency?
50-60 years
Table 2.1 in the textbook shows the data of the number of different Walmart departments each customer buys from (automotive, grocery, sports, camping, etc.). At most, one customer will buy from 11 different departments (whew, that is a lot of walking!). What is the frequency of one customer buying from 11 different departments?
7
Which is an example of how probability is used in business?
A TV manufacturer wants to offer an warranty on its TV, but it wants to know the chance that it will have to reimburse the consumer because the TV breaks.
What does a scatter diagram, or a scatter plot, show?
A graph that show two variables simultaneously
What is the difference between a median and a mode?
A median is the center value that divides data into 2 halves. A mode is value in the dataset that occurs most frequently.
What is the difference between a population and a sample?
A population includes all objects or individuals of interest; a sample is a subset of the population.
Which of the following does not apply to a random variable?
A random variable is known with certainty
What does the following equation represent? x bar - u
A sampling error
What is the difference between a parameter and a statistic?
A statistic such as the mean is computed from the sample data. A parameter is the population's mean, for example.
In the scatter plot below, what is the relationship between the temperature outside and sales of ice cream?
Basically Linear
Why is it important that we can assume that the sample drawn from a population is normally distributed?
Because then we can use the standardized z-value and analysis using the z-value and standard normal table of probabilities.
When you are trying to find the confidence interval estimate for the population mean and the standard deviation is NOT known, why do we use the t-distribution and not the standard normal distribution (and z-values)?
Because we are estimating the standard deviation (sigma), and adding more uncertainty to our estimate, we need a distribution that is more spread out.
How is conditional probability defined?
Chances of two or more events occurring in succession.
Which of the following describes nominal data?
Codes are assigned to categories
In the population of Americans, the average height is 5 feet 8 inches. If we take a sample of 200 Americans, we might find that the sample mean is 5 feet 6 inches. There will always be a sampling error whereby the sample mean will not exactly match the population mean. To overcome this difference, problem with point estimates, we calculate a ________________________.
Confidence interval
Two elements that are first needed to decide the necessary sample size are __________________and ____________________.
Confidence level; desired margin of error
Which of the following does not define estimation?
Correct: Estimation is a technique that takes the entire population of data to examine the data. Estimation is a technique that takes a smaller subset of a larger population of data to get an idea of what the entire population looks like. Estimation is used when we would like to know about all the data in a large dataset but it is impractical to work with all the data.
Which is the correct order for the major steps of developing a survey?
Define the issue, define the population of interest, design the survey instrument, pretest the survey, determine the sample size and method, select the sample, send survey
The Binomial Distribution in one in which ....
Describes a process (experiment) with two possible outcomes, success and failure
Which of the following is the correct formula of expected value of a discrete probability distribution?
E(x) = ∑xP(x)
What are the two primary categories of statistical inference procedures? Inference means to draw some useful conclusions from the raw data that can help improve business decisions.
Estimation and hypothesis testing
An experiment is a process that produces a single outcome whose result can be predicted with certainty.
False
Bayes' Theorem uses old, historical information to update your estimated probabilities.
False
Estimating a population parameter based on a sample statistic is one area of business statistics called statistical influence.
False
For any population, the average value of all possible sample means computed from ALL possible random samples of a given size from the population does not equal the population mean.
False
If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form: H0 : μ = 100 HA : μ ≠ 100 will result in a one-tailed hypothesis test since the sample result can fall in only one tail.
False
If a hypothesis test leads to incorrectly rejecting the null hypothesis, a Type II statistical error has been made.
False
In the graph below, Time is the y-axis and the x-axis is Temperature.
False
Missing data is never a problem when running some numeric measures in Excel.
False
Proportions can be thought of as a discrete binomial distribution (with one or two known possible outcomes), but if the sample size is large enough, proportions can be assumed to be distributed as an exponential distribution
False
Qualitative data refers to data such as numbers (dollars, pounds, inches, or percentages).
False
You are a statistician calculating the necessary sample size for a client. Which of the following data is necessary to calculate necessary sample size?
Margin of error; z-value; population standard deviation
Under Course News you will find the Greek Alphabet. We will be using a lot of these letters in this class. How is the Greek letter for mean, or average, pronounced?
Mu
If a survey is conducted of consumers preferences for a new soda and 1= Love it!, 2=It's okay, 3=Don't like it, then what type of data is this?
Nominal
Which of the following is the correct ranking of data from the lowest level of basic analysis to the highest?
Nominal, ordinal, ratio/interval
CMU wants to survey students about what they think of the CMU grounds (grass, trees, sidewalks) so CMU officials stop students coming and going from the Davis Business School. What kind of sampling is this?
Nonstatistical
Which of the following is not a statitical sampling technique? Simple random sampling Systematic random sampling Cluster sampling Not-so-simple random sampling
Not-so-simple random sampling
Graphs and charts are great -- very informative -- but you can describe the data even more thoroughly with the use of ________________.
Numerical measures
The government is doing a study of how much ticket holders pay for basketball games across the U.S. There is only a limited budget to do the survey so the statistician divides stadiums into three groups: small, medium, and large stadiums and then takes a random sample from each of these groups. Which kind of sampling procedure is this?
Stratified random sample
The owner of a local gasoline station has kept track of the number of gallons of regular unleaded sold at his station every day since he purchased the station. This morning, he computed the mean number of gallons. This value would be considered a .....
Parameter Parameter because all the data is available, the entire population not just a sample of data of the population
The sample shoe size computed from 200 women is 8.0. The value 8.0 is a _________of the population mean, mu.
Point estimate
The circle on the left is called a __________________ and the circle on the right is called a ___________________.
Population; sample
Which of the following is NOT an advantage of a written survey?
Potentially Low Response Rate (5-10%)
Convert the frequency distribution into a probability distribution using the relative frequency method (Hint: Example 5-1). Here are the results of a survey. I make ice cream. I buy 20 gallons of cream to make ice cream each week. The following is the number of gallons each week that are sour and not usable.
Probabilities are: for 0 gallons = 0.5, for 1 gallons = 0.25, for 2 gallons = 0.20, for 3 gallons = 0.05.
What is the following diagram called?
Probability tree
According to the bar chart below, in which quarter (Q1, Q2, etc.) did the city of York , have a higher new revenue than that of Lincoln or Mersey?
Q4
A hair salon is interested in sampling its customers about its hair dye services. It knows that 80% of its customers are female, so its makes sure that 80% of its survey sample is female. What kind of sampling is this?
Ratio
Which of the following is NOT a method for collecting data?
Reading tea leaves
In which of the following sampling procedures does each possible observation in the population have an equal chance of being selected?
Simple random sample
If I take a survey at my kids' school of ages, which measure would tell me how spread out the ages are from the young kids to the older kids.
Standard deviation
Fill in the blank with the best answer. The _______________ introduced in this text are those that help transform data into information.
Statistical procedures
A grocer wants to take a consumer satisfaction survey among value consumers with value cards. So the grocery manager selects that kth consumer among her valued customers (ones with value ID numbers).
Systematic random sample
A frequency histogram can be directly constructed from _________________.
The frequency distribution table (how many times each observation shows up).
In Chapter 6. we study the expected value of a discrete probability distribution. Another way to describe the expected value of a discrete probability distribution is...
The mean -- the expected average probability of a distribution
Which of the following does not apply to an estimate? The use of techniques to get an idea of what a larger data set looks like The population of all of CMU students The percent of CMU students that say they drink coffee daily from a survey of 10 in this class Looks at a subset of the larger data set
The population of all of CMU students
In words, what does P(E) mean?
The probability of event E occurring.
How is a joint probability defined?
The probability of two separate events occurring at the same time.
Which of the following does not interject bias into a survey question?
The professional dress of the guy/gal running the survey
There are three approaches to hypothesis testing, all which produce the same results.
True
The Empirical Rule can tell you which of the following?
The values (a low and high value) in which 68% of your population's values fall.
Why is it sometimes important to calculate the weighted meaninstead of an arithmetic mean?
The weights may make the weighted mean very different from the arithmetic mean.
If a sample mean is 108.50 and a population mean is 25.50, then which of the following is true?
This sample would be a misleading value for the center of the population.
Chapter 8. introduces the t-distribution. When is the t-distribution used?
To find the confidence interval estimate for a population mean when the standard deviation (sigma) of the population is not known
A histogram displays the shape and spread of the distribution of data.
True
A hypothesis test tests claims about products or services using information taken from samples.
True
A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles. If a consumer group wished to test this claim, the research hypothesis would be: Ha : μ > 80,000 miles.
True
A sampling error is the difference between a measure computed from a sample (a statistic) and the corresponding measure computed from the population (a parameter).
True
As the sample size increases, we can expect the value of the statistic to become closer to the parameter, which means the statistic is a consistent estimator of the parameter.
True
Business statistics can be split into two fields. The first category describes the data (charts, graphs, numerical measures). The second category includes tools and techniques that help decision makers draw inferences from a set of data.
True
Descriptive Statistics and Inferential Procedures are two categories of business statistics.
True
Graphs and charts are excellent ways to "show" your data. Reading a table of numbers is hard, you don't get a lot out of it, but put in into a chart/graph and whoa, you are now telling a story about values, frequencies and trends.
True
In Chapter 8. we don't know the population parameter such as its mean, mu, but we want to estimate it through sampling, and thus want to find the sample statistics that hopefully come close to the population parameters.
True
In a one-tailed test (upper tail), if the sample mean is inconsistent (higher) than the null hypothesis, we reject H0
True
In hypothesis testing, the null hypothesis should contain the equality sign.
True
In most of your classes (I assume) your grades are calculated using a weighted mean, not an arithmetic mean.
True
In this class, we will learn procedures of how to transform data into useful information.
True
Just like previous discussions in which we want our sample to represent our population, you want your sample proportion to represent your population proportion.
True
Larger sample sizes result in less variability in the distribution of sample means.
True
Standardized data values are particularly helpful when we wish to compare data form two or more distributions when the data scales for the two distributions are very different.
True
Statistical sampling allows every item in the population to have a known or calculable chance of being included in the sample.
True
The following is an example of a Binomial Distribution. A survey is conducted of 100 people and the consumers respond, "Yes, I love your new product," or "No, I don't like your new product."
True
The greater the difference between the mean and median, the more skewed the distribution.
True
The margin of error is the amount by which the point estimate differs from the population mean. You will not get a sample mean from a sample that is exactly equal to the population mean, but you can close, with some margin of error.
True
The significance level in a hypothesis test corresponds to the maximum probability that a Type I error will be committed.
True
How are relative frequencies calculated?
You divide the frequency in a category by the total number of observations.
We use graphs/charts to communicate with .... Customers Employees Suppliers in business All of the above
all of the above
Which of the following can introduce bias into your survey? Conducting the survey at 3 am in the morning. Starting the question with, "You look like you are smart and would agree with ...." Conducting an online survey in an area with very spotty internet service. All of the above.
all of the above
Equation (8.5) shows the formula for the _____________________when the population standard deviation is unknown.
confidence interval estimate for the population mean
In order to find the confidence interval estimate for a population proportion (p) you need the following....
p bar, z-value, n
The population standard deviation is denoted by Sigma. What is the sample standard deviation denoted by?
s
Which of the following does not apply to business statistics/business intelligence? computer science is among the fastest-growing career areas small business management statistics
small business management
The z-value represents the number of standard deviations a point is above or below the population mean in a normal distribution. The mean check out time at a grocery stores nationally (the entire population of grocery stores) is 8 minutes. The standard deviation of check out time is 3 minutes. A survey was conducted at a local grocery store in order to compare itself to the national average. It found that the check out time 10 minutes. Compare this check out time to the population average. Convert your answer to two decimal places. Hint: Follow the Business Application , EMT Response Times, page 215 and use the Excel formula page 215.
z-value = 0.67; The check out time at the local grocery store is 0.67 standard deviations above the population mean