Probability
It is known that 15% of seniors in a large high school enter military service upon graduation. If a group of 20 seniors are randomly selected, what is the probability of observing at most one senior who will be entering military service?
A large suburban school wants to assess student attitudes towards their mathematics textbook. The administration randomly selects 25 students from each grade and gives the survey to those students. This is an example of a ___ sample.
Suppose the correlation between two variables x and y is r = -0.24. If each x variable is doubled and each y variable is increased by 0.1, and the two variables are then interchanged, what is the new correlation?
A set of data has a mean that is much larger than the median. What does that tell you about the distribution?
The weight of an aspirin table is 300 mg according to the bottle label. An FDA investigator weights a SRS of 7 tablets, obtains weights of 299, 300, 305, 302, 299, 301, and 303 and runs a hypothesis test of the manufacture's claim. Is the weight different? What is the p-value of this test?
The wait to get through a bridge’s toll booth complex at rush hour is 3 minutes, 45 seconds with a standard deviation of 58 seconds. What is the probability that the next 25 cars in line have to wait on average more than 4 minutes? Assume normality of waiting times.
We wish to draw a sample of size 5 without replacement from a population 50 households. Suppose the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is:
11362 35692 96237 90842 46843 62719 64049
What is the number of the fourth house selected for the sample?
On a project where x is defined as the age of a particular type of car in years and y is the Kelly Blue Book Value of the vehicle, it is found that the standard deviation of x is 3.5, the standard deviation of y is 4,650 and r = -0.91. Find the slope.
Students enter their essays in a contest in order to compete for a prize. Each essay is read by the same number of judges. Doug’s essay has a different score from each judge. If the lowest score for Doug was eliminated, which of the following would definitely change?
I. The mean
II. The median
III. The standard deviation
A company wants to evaluate the effectiveness of a new drug for combating acne. What sample size should the company use in order to estimate the proportion of users who would experience an improvement within 4% of the true proportion with 95% confidence?
A local fast-food restaurant is advertising one of its new combo means and is offering one of four prizes with each meal purchased. A prize will be placed at random in each combo meal bag. One of the prizes, a ticket for an upcoming popular concert tour is more rare than the other prizes and occurs in only 5% of the bags. What is the probability that the sixth combo-meal purchased will be the first time to you win a concert ticket?
A sample of n = 14 pairs of identical twins are volunteers in an experiment studying the benefits of exercise on resting heart rate. What is the most appropriate design for this experiment?
Which of the following statements are correct?
1. The correlation r is the slope of the LSRL
2. The square of the correlation is the slope of the LSRL.
3. The square of the correlation is the proportion of the data lying on the LSRL
4. The coefficient of determination is the fraction of variability in y that can be explained by the LSRL of y on x.
5. The sum of the squared residuals from the LSRL is zero.
The proportion of observations from a standard normal distribution that take values larger than z =0.75 is about:
Researchers working for the drug company “Risky Business” have developed a new cough medicine called “Cough-No-Mor” that “significantly reduces the time that a cough will be with you.” They are required by the Federal Food and Drug Administration (FDA) to thoroughly test the drug. They use proper experimental design attempting to either reduce or eliminate confounding errors. What steps should they take to increase the power of their experiment?
A large taxi company has 20% Chevy’s, 35% Fords, and the rest are foreign cars. The probability that a taxi will fail to start on a cold winter day is .04, .02, and .006 respectively, depending on whether it is a Chevy, Ford, or foreign. If a randomly chosen taxi fails to start, what is the probability that it is a foreign car?
A television station broadcast a court trial in its entirety. During a news program, viewers were asked to go to the TV station’s website and state whether they thought the defendant was guilty or not guilty. Of the 1,840 viewers who gave their opinion, 1,521 felt that the defendant was not guilty. The viewers who registered their opinions constitute a _____ sample.
A psychologist determines that a strong, positive linear relationship exists between an individual's IQ score and their sense of humor. She randomly selected 45 adults and found the following results:
IQ: mean = 105, standard deviation = 12
Test of Humor: Mean = 140, standard dev. = 24
r2 = 0.81
What is the predicted humor score if the IQ score of an individual is 110?
Niagara Falls, New York and Niagara Falls, Ontario are right across the Niagara River from each other, less than a mile away and so obviously get the same weather. However, Niagara Falls, New York measures temperature in degrees Fahrenheit and Niagara Falls, Ontario measures temperatures in degrees Celsius. Suppose the average temperature for a month in Niagara Falls, Ontario is 30 degrees C. with a standard deviation of 1.7 degrees. What would be the reported mean and standard deviation in degrees Fahrenheit for Niagara Falls, New York?
F=9/5C + 32
The analysis of a random sample of 1,000 diners at the chain InFront Steakhouse with many restaurants throughout the country indicates that a 95% confidence interval for the mean percent tip is (14.23%, 18.79%).
Use this information to conduct a hypothesis test at the 5% level that people tip 18% at this restaurant. What is your conclusion?
Distribution X is normal with a mean of 25 and standard deviation of 4. Distribution Y is normal with a mean of 22 and standard deviation of 3. Find the probability a randomly selected value of Y is greater than a randomly selected value of X.
What is .2743
The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and then determines the proportion of the 150 controllers that are defective. This is an example of a ___ sample.
Let x be the number of subway stops your destination is from here and y be the amount of time in seconds to reach your stop.
Use this formula: y=89.2x-13.4 r=0.87
A trip of 12 subway stops took me 16.5 minutes. What is the residual of the time for my trip in minutes?
A certain model car sells on average nationwide at $19,525. About 12% of the dealerships in the country sell the car for above $20,000. What is the approximate standard deviation of the nationwide prices for this car, assuming normality of prices?
In a simple random sample, 87 of 93 said they were happy with their iPod Touch MP3 player while 48 of 62 said they were happy with their Zune MP3 player. Find a 95% confidence interval estimate for the difference between IPod and Zune owners who are satisfied with their MP3 player.