ECO 250 Final Exam | Complete Solution

Be sure to round answers to at least two decimals! You will not get credit for the answer 3.1 if the actual answer is 3.1157, but you would get credit for 3.12, 3.116, or 3.1157.

 
Question 1 
The mathematical science that deals with the collection, analysis, and presentation of data is 
 
Economics 
 
Mathematical analysis 
 
Statistics 
 
Data analysis 
 
Question 2 
Sampling error is the difference between the __________ and the parameter. 
 
Sample 
 
Sample mode 
 
Statistic 
 
None of the above 
 
 
Question 3 
The __________ is the probability distribution used in place of the normal distribution to calculate a confidence interval when the population standard deviation is unknown. 
 
Uniform distribution 
 
Binomial distribution 
 
Exponential distribution 
 
Student's t-distribution 
 
 
Question 4 
A __________ is a distribution in which the probability of any interval occurring is equal to any other interval with the same width. 
 
Normal distribution 
 
Uniform distribution 
 
Binomial distribution 
 
Student's t-distribution 
 
 
Question 5 
The number of rushing touchdowns for the Minnesota Vikings in a season is an example of 
 
Nominal data 
 
Ratio data 
 
Interval data 
 
Ordinal data 
 
Question 6 
Which is a continuous random variable? 
 
The number of students in an ECO 250 class. 
 
The number of births in a hospital on a given day. 
 
The hourly earnings of a call center employee in Boston. 
 
The number of fives obtained in four rolls of a die. 
 
 
Question 7 
The empirical rule states if a distribution is symmetrical and bell-shaped, approximately 68%, 95%, and _______ of its data values will fall within one, two, and three standard deviations above and below the mean, respectively. 
 
99.5% 
 
98% 
 
99.7% 
 
99% 
 
 
Question 8 
__________ is the probability that the interval estimate will include the population parameter of interest, such as a mean. 
 
Significance level 
 
Confidence level 
 
Degrees of freedom 
 
Margin of error 
 
 

Question 9 
The __________ is a variable that represents the probability that any given confidence interval will not contain the true population mean. 
 
Significance level 
 
Degrees of freedom 
 
Confidence level 
 
Margin of error 
 
 
Question 10 
What is an error that occurs when the null hypothesis is rejected when, in reality, it is true? 
 
None of the above 
 
Type I error 
 
Sampling error 
 
Type II error 
 
Question 11 
Which is a time series variable? 
 
VISA balances of 30 students on December 31 of this year. 
 
Dollar exchange rates yesterday against 10 other world currencies 
 
Net earnings reported by Xena Corp for the last 10 quarters. 
 
Titles of the top 10 movies in total revenue last week 
 
 
Question 12 
A tire company performs quality-control tests on the monthly output of its best-selling model tire at each of its plants. Each month a random sample of 25 tires is selected from each plant and tested to see if the average tread life of that plant’s tires is above specifications. For one plant, the random sample of 25 tires had a sample mean of 39,500 miles and a sample standard deviation of 3,300 miles. The company performs a hypothesis test at the .05 level of significance to see if there is evidence that the average tread life is greater than 38,000. Based on this sample, the company should: 
 
Reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles. 
 
Fail to reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles. 
 
Reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles. 
 
Fail to reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles 
 
Question 13 
What is the probability of observing a sample mean at least as extreme as the one selected for the hypothesis test, assuming the null hypothesis is true? 
 
p-value 
 
Alpha 
 
Beta 
 
Confidence level 
 
 
Question 14 
Which is not a characteristic of a binomial experiment? 
 
The experiment consists of an infinite number of trials. 
 
Each trial has only two possible outcomes: a success or a failure 
 
Each trial is independent of the other trials in the experiment 
 
The probability of success is equal to one minus the probability of failure 
 
 
Question 15 
A __________ is a continuous distribution that is bell shaped and symmetrical around the mean. 
 
Exponential distribution 
 
Normal distribution 
 
Uniform distribution 
 
Binomial distribution 
 
 
Question 16 The critical z-score for an 85% confidence level is ________. 
 
 1.44 
 
 1.28 
 
 2.33 
 
 1.96 
 
 

Question 17 
YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 6 minutes. A random sample of 40 people watched online videos that averaged 6.6 minutes in length. The population standard deviation for the length of online videos is 1.7 minutes. YouTube would like to set  α=0.05. The p-value for this hypothesis test would be _________. 
 
0.0644 
 
0.0395 
 
0.0129 
 
0.0268 
 
Question 18 
A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. The correct hypothesis statement would be 
 
 
 
 
 
 
 
 
 
 
 
 
Question 19 
What should you do when the p-value is less than the significance level? 
 
Fail to reject the null hypothesis 
 
Accept the alternative hypothesis 
 
Accept the null hypothesis 
 
Reject the null hypothesis 
 
 
Question 20 
Consider the following set of numbers: 10, 25, 13, 18, 40, 5. Determine the median and variance of these data. 
 
median = 18.5, variance = 12.57 
 
median = 15.5, variance = 157.9 
 
median = 15.5, variance = 35 
 
median = 18.5, variance = 473.83 
 
 
Question 21 
A point estimate, also called a statistic, is a single value that describes the population of interest, with the sample mean being the most common. 
 
True 
 
False 
 
 
Question 22 
The margin of error is the width of the confidence interval between the lower limit and the upper limit. 
 
True 
 
False 
 
 
Question 23 
The alternative hypothesis represents the status quo and involves stating the belief that the population parameter is   a specific value and is always associated with the equal sign. 
 
True 
 
False 
 
 
Question 24 
A z-score measures the number of standard deviations a value is from its mode. 
 
True 
 
False 
 
 
Question 25 
Suppose Nike's average stock price this year is $15.00 with a standard deviation of $3.00, and Under Armour's average stock price this year is $24.00 with a standard deviation of $4.00. According to this data, Nike's stock price is more consistent than Under Armour's stock price. 
 
True 
 
False 
 
 
Question 26 
The Central Limit Theorem states that sample means, drawn from a normally distributed population, will be normally distributed. 
 
True 
 
False 
 
 
Question 27 
A low p-value indicates a high probability that the null hypothesis is not true. 
 
True 
 
False 
 
Question 28 
If the absolute value of the test statistic is less than the critical value in a two-tailed hypothesis test, then the decision is to reject the null hypothesis. 
 
True 
 
False 
 
 
Question 29 
Consider the hypotheses
H0: Defendant is innocent
H1: Defendant is guilty
If a court acquits every defendant, they will never commit Type II error.
 
True 
 
False 
 
 
Question 30 
If we do not have evidence to support the alternative hypothesis, then we accept the null hypothesis. 
 
True 
 
False 
 

Question 31 
Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. What are your null and alternative hypotheses? 
 
 
 
 
 
 
 
 
 
 
 
Question 32 
Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Calculate the test statistic for the sample data. 
 
 
 
Question 33 
Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. State the critical value. 
 
 
 
Question 34 
Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Determine whether or not the null hypothesis should be rejected. 
 
Fail to reject the null hypothesis. 
 
Reject the null hypothesis. 
 

Question 35 
Consider the following data on the number of beers consumed by a sample of football fans during a game:
3       5       0       2       5       3.
 
Calculate the mean number of beers.
 
 
Question 36 
Consider the following data on the number of beers consumed by a sample of football fans during a game:
3       5       0       2       5       3.
 
Calculate the median.
 
 
 
Question 37 
Consider the following data on the number of beers consumed by a sample of football fans during a game:
3       5       0       2       5       3.
Calculate the mode (mark all that apply).
 
0 
 
5 
 
2 
 
3 
 

Question 38 
Consider the following data on the number of beers consumed by a sample of football fans during a game:
3       5       0       2       5       3.
Calculate the variance.
 
 
 
Question 39 
You check the weather forecast every morning. On average, it is rainy 20 percent of the time. Consider the next 5 days. What is the probability it will be rainy exactly 1 day? 
 
 
Question 40 
You check the weather forecast every morning. On average, it is rainy 20 percent of the time. Consider the next 5 days. What is the probability it will be rainy at most 2 days? 
 
 

 
Question 41 

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the margin of error (in hours) for the 90% confidence interval for this sample. 
 
 

Question 42 

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the lower confidence limit (LCL), in hours, for the 90% confidence interval for this sample. 
 
 

Question 43 

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the upper confidence limit (UCL), in hours, for the 90% confidence interval for this sample. 
 
 

 
Question 44 

Consider the following discrete probability distribution.
    X            P(X)    
0    0.2
1    0.3
2    0.4
3    0.1
Total    1.0
Calculate the mean of this distribution.
 
 

 
Question 45 
Consider the following discrete probability distribution.
    X            P(X)    
0    0.2
1    0.3
2    0.4
3    0.1
Total    1.0
Calculate the variance of this distribution.
 
 Question 46 

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.
What is the mean of this distribution?
 
 
Question 47 
The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.
What is the probability that the employee's next commute to work will require less than 10 minutes?
 
 
Question 48 
The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.
What is the probability that the employee's next commute time will require between 12 minutes and 20 minutes?
 
 
Question 49 
Consider the following hypothesis:
 
 H1: μ>25
Given that   calculate the test statistic.
 
 

Question 50 
Consider the following hypothesis:
 
 H1: μ>25
Given that   state the critical value.
 
 

Question 51 

Consider the following hypothesis:
 
 H1: μ>25
Given that   determine whether or not the null hypothesis should be rejected.
 
Fail to reject the null hypothesis 
 
Reject the null hypothesis 
 

Question 52 

A tire manufacturer selected a random sample of 50 tires of a particular model chosen from the past month’s production and used destructive testing to determine the tread life of each tire. The sample mean was 42,300 miles and the sample standard deviation was 7,500 miles. What is the 95% confidence interval estimate for the tread life of that entire model produced in the past month? 
 
 
 
 
 
 
 
 
 
 
 
 
 

Question 53 

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.
What is the probability of exactly four complaints during the next four weeks?
 
 

Question 54 

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.
What is the probability of four or more complaints during the next four weeks?
 
 

Question 55 

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.
What is the probability of exactly three complaints during the next two weeks?
 
 

 
Question 56 

Zombies eat, on average, 5 brains per day. Assume the actual number of brains eaten per day follows the normal distribution with a standard deviation of 0.29 brains. What is the probability that a zombie will eat exactly 3.2 brains tomorrow?