# Statistics Answers for BUS 475 Final Exam 2017

### You work in marketing for a company that produces work boots.

Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard deviation of 14 days. For an upcoming ad campaign, you need to know the percent of the pairs that last longer than six months-that is, 180 days. Use the empirical rule to approximate this percent.

97.5%

Explanation: This question is asking how many pairs of boots will NOT  fail at 2 standard deviations before the mean 208 days. Using the empirical rule, we know that 2 standard deviations is equal to 2.5% of the population on each tail, therefore 2.5%. Subtract this value from 100% and we get 97.5% of boots will last longer then six months.

• Student: Barry Tadworth
• Textbook: Multiple Textbooks Combined
• Course: BUS 475 (2017-18)

### What is an advantage of the correlation coefficient over the covariance?

It falls between -1 and 1; and it is a unit free measure, therefore making it easier to interpret.

Explanation: The correlation coefficient does fall between -1 and 1, the sigmoid range, and can be interpreted for any datatype because it is unit free. For instance, units in kilometers and miles could be compared on the same scale.

### Which of the following meets the requirements of a simple random sample?

A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age.

Explanation: A simple random sample must choose randomly from the entire population distribution without altering the parameters. In this case, sampling without regard to age is the correct approach.

### Sampling is used heavily in manufacturing and service settings to ensure high-quality products

In which of the following areas would sampling be inappropriate?

Custom cabinet making

Explanation: Because all custom cabinets are produced differently, it would not be appropriate to sample for quality control.

### In multiple regression, plot the residuals against ____ to detect changing variability

All explanatory variables

Explanation: In a regression, the residuals are the comparisons between the response and predicted values. You can plot these against all explanatory variables to detect changes in variability.

### For both qualitative and quantitative data, what is the difference between the relative frequency and the percent frequency?

As opposed to the relative frequency, the percent frequency is divided by the number of observations in the data set.

Explanation: Percent frequency is simply the relative frequency concerted to a range of 0 to 100%. This can be done by taking a frequency number and dividing by the observations in the data set.

### In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate?

Zero 0

Explanation: If all data points are perfectly aligned with the regression line, the error would be zero. In other words, the regression is perfect at predicting the the value of the data and has no error.

### Is it possible for a data set to have no mode?

Yes.

Explanation: The mode will only exist if there are more than 1 data points with the same value.

### Which of the following can be represented by a discrete random variable?

The number of defective light bulbs in a sample of five

Explanation: Discrete variables can be counted, but not measured. If a measurement can be taken with infinite precision, such as the time of a flight took 4.55523234232342 hours, then it is continuous (not discrete).

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