Mind on Statistics
Mind on Statistics
5th Edition
ISBN: 9781285463186
Author: Jessica M. Utts, Robert F. Heckard
Publisher: Brooks Cole
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Chapter 8, Problem 8.1E

(a)

To determine

To find: Whether the given variable is discrete or continuous.

(a)

Expert Solution
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Answer to Problem 8.1E

The given variable is discrete.

Explanation of Solution

Given:

The variable is “Number of commercials that are shown”.

A variable whose value is determined by counting is referred to as a discrete variable. A continuous variable is one whose value may be determined through measurement.

In this case, the given variable, the number of commercials shown, can be counted and does not take unrounded values. Thus, it can be considered an example of a discrete random variable.

Therefore, the variable is a discrete variable.

(b)

To determine

To find: The given variable is discrete or continuous.

(b)

Expert Solution
Check Mark

Answer to Problem 8.1E

The given variable is continuous.

Explanation of Solution

The given variable is the length which is noted in seconds. The variable's length can take any value within a certain range. The length of the commercial cannot be counted; it takes unrounded values. Thus, it can be considered a continuous random variable.

Therefore, the variable is continuous.

(c)

To determine

To find: The given variable is discrete or continuous.

(c)

Expert Solution
Check Mark

Answer to Problem 8.1E

The given variable is discrete.

Explanation of Solution

In this case, the given variable is the number of accidents recorded. The variable can only have two values that can be counted and do not take unrounded values. Thus, it can be considered an example of a discrete random variable.

Therefore, the variable is discrete.

(d)

To determine

To find: The given variable is discrete or continuous.

(d)

Expert Solution
Check Mark

Answer to Problem 8.1E

The given variable is discrete.

Explanation of Solution

In this case, the given variable is whether the rain is predicted. The variable can only have two values that can be counted and do not take unrounded values. Thus, it can be considered an example of a discrete random variable.

Therefore, the variable is discrete.

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To  evaluate  the  success  of  a  1-year  experimental  program  designed  to  increase  the  mathematical achievement of underprivileged high school seniors, a random sample of participants in the program will be selected and their mathematics scores will be compared with the previous year’s  statewide  average  of  525  for  underprivileged  seniors.  The  researchers  want  to  determine  whether the experimental program has increased the mean achievement level over the previous year’s statewide average. If alpha=.05, what sample size is needed to have a probability of Type II error of at most .025 if the actual mean is increased to 550? From previous results, sigma=80.

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