In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of Illumination,” J. Illuminating Eng., 1976: 235–242), subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid succession both for a low light level with a black background and a higher level with a white background. Each data value is the time (sec) required to complete the task.
\(\begin{array}{|c|c|} \hline Subject & (1) & (2) & (3) & (4) & (5) &(6) & (7) & (8) & (9) \\ \hline Black & 25.85 & 28.84 & 32.05 & 25.74 & 20.89 & 41.05 & 25.01 & 24.96 & 27.47 \\ \hline White & 18.28 & 20.84 & 22.96 & 19.68 & 19.509 & 24.98 & 16.61 & 16.07 & 24.59 \\ \hline \end{array}\)
Does the data indicate that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time? Test the appropriate hypotheses using the P-value approach.
The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer ("A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age," Quality and Reliability Engr. Intl.,
a) can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. [Note: A normal probability plot of data exhibits a reasonably linear pattern.]
b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean
An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.
Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.
Aurora intends to take part in a competition during her school's field day where she must finish tasks at several stations as quickly as she can. She's practicing and timing herself as she completes each station to get ready for the competition. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5.
Part C: Use an explicit formula to find the time she will complete the 9th station.