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Time required to complete a task. When a person is asked,
Chapter 7, Problem 39E(choose chapter or problem)
Time required to complete a task. When a person is asked, “How much time will you require to complete this task?” cognitive theory posits that people (e.g., a business consultant) will typically underestimate the time required. Would the opposite theory hold if the question was phrased in terms of how much work could be completed in a given amount of time? This was the question of interest to researchers writing in Applied Cognitive Psychology (Vol. 25, 2011). For one study conducted by the researchers, each in a sample of 40 University of Oslo students was asked how many minutes it would take to read a 32-page report. In a second study, 42 students were asked how many pages of a lengthy report they could read in 48 minutes. (The students in either study did not actually read the report.) Numerical descriptive statistics (based on summary information published in the article) for both studies are provided in the accompanying table.
\(\begin{array}{lcc}
\hline & \begin{array}{c}
\text { Estimated } \\
\text { Time (minutes) }
\end{array} & \begin{array}{c}
\text { Estimated } \\
\text { Number of.Pages }
\end{array} \\
\hline \text { Sample size, } n & 40 & 42 \\
\text { Sample mean, } \bar{x} & 60 & 28 \\
\text { Sample standard } & 41 & 14 \\
\quad \text { deviation, } s & & \\
\hline
\end{array}\)
a. The researchers determined that the actual mean time it takes to read the report is \(\mu=48\) minutes. Is there evidence to support the theory that the students, on average, overestimated the time it would take to read the report? Test using \(\alpha =.10\).
b. The researchers also determined that the actual mean number of pages of the report that is read within the allotted time is \(\mu=32\) pages. Is there evidence to support the theory that the students, on average, underestimated the number of report pages that could be read? Test using \(\alpha=.10\).
c. The researchers noted that the distribution of both estimated time and estimated number of pages is highly skewed (i.e., not normally distributed). Does this fact impact the inferences derived in parts a and b? Explain.
Questions & Answers
QUESTION:
Time required to complete a task. When a person is asked, “How much time will you require to complete this task?” cognitive theory posits that people (e.g., a business consultant) will typically underestimate the time required. Would the opposite theory hold if the question was phrased in terms of how much work could be completed in a given amount of time? This was the question of interest to researchers writing in Applied Cognitive Psychology (Vol. 25, 2011). For one study conducted by the researchers, each in a sample of 40 University of Oslo students was asked how many minutes it would take to read a 32-page report. In a second study, 42 students were asked how many pages of a lengthy report they could read in 48 minutes. (The students in either study did not actually read the report.) Numerical descriptive statistics (based on summary information published in the article) for both studies are provided in the accompanying table.
\(\begin{array}{lcc}
\hline & \begin{array}{c}
\text { Estimated } \\
\text { Time (minutes) }
\end{array} & \begin{array}{c}
\text { Estimated } \\
\text { Number of.Pages }
\end{array} \\
\hline \text { Sample size, } n & 40 & 42 \\
\text { Sample mean, } \bar{x} & 60 & 28 \\
\text { Sample standard } & 41 & 14 \\
\quad \text { deviation, } s & & \\
\hline
\end{array}\)
a. The researchers determined that the actual mean time it takes to read the report is \(\mu=48\) minutes. Is there evidence to support the theory that the students, on average, overestimated the time it would take to read the report? Test using \(\alpha =.10\).
b. The researchers also determined that the actual mean number of pages of the report that is read within the allotted time is \(\mu=32\) pages. Is there evidence to support the theory that the students, on average, underestimated the number of report pages that could be read? Test using \(\alpha=.10\).
c. The researchers noted that the distribution of both estimated time and estimated number of pages is highly skewed (i.e., not normally distributed). Does this fact impact the inferences derived in parts a and b? Explain.
ANSWER:Step 1 of 4
Here, the experiment under consideration is study of time required to read certain pages of a document.
In one study 40 students were asked how many minutes they would take to read a 32-pages report.
In another study, 42 students were asked how many pages they could read in 48 minutes.
The descriptive statistics for the obtained data for the two study is given.
\(\begin{array}{|l|l|l|}
\hline & \text { Estimated time(minutes) } & \text { Estimated number of pages } \\
\hline \text { Sample size,n } & 40 & 42 \\
\hline \text { Sample mean } \bar{x} & 60 & 28 \\
\hline \text { Sample standard deviation,s } & 41 & 14 \\
\hline
\end{array}\)
Using this data we need to find the required values.