In an experiment designed to study the effects of illumination level on task performance (“Performance of Complex Tasks Under Different Levels of

Nann 2021-03-07 Answered

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.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Lacey-May Snyder
Answered 2021-03-08 Author has 88 answers

Given:
n=Sample size=9
Given claim: Mean difference is more than 5
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis and the alternative hypothesis state the opposite of each other. The null hypothesis needs to contain the value mentioned in the claim.
H0:μd=5
Ha:μd>5
Let us first determine the difference between each pair of data values:
Population1Population2Differenced25.8518.2325.8518.23=7.6228.8420.8428.8420.84=8.0032.0522.9632.0522.96=9.0925.7419.6825.7419.68=6.0620.8919.5020.8919.50=1.3941.0524.9841.0524.98=16.0725.0116.6125.0116.61=8.4024.9616.0724.9616.07=8.8927.4724.5927.4724.59=2.88
Determine the sample
Determine the sample mean of the differences. The mean is the sum of all values divided by the number of values.
d¯=7.62+8.00+9.09++8.89+2.8897.6
Determine the sample standard deviation of the differences:
sd=(7.627.6)2++(2.887.6)2914.1779
Determine the value of the test statistic:
t=d¯dsdn=7.654.177991.867
The P-value is the probability of obtaining the value of the test statistic, or a value more extreme, assuming that the null hypothesis is true. The P-value is the number (or interval) in the column title of the Students T distribution in the appendix containing the t-value in the row df=n1=91=8
0.025<P<0.05
If the P-value is less than the significance level, reject the null hypothesis.
P<0.05Reject H0
There is sufficient evidence to support the claim that the higher level of illumination yields a decrease of more than 5 sec in true average task completion time.

Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-01-06
A weather forecaster predicts that the temperature in Antarctica will decrease 8F each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36F
asked 2021-02-25

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. (1,3),(2,6),(3,12),(4,24)
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.

asked 2021-03-07
A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point (4, 5). Write an equation that represents the path.
asked 2020-11-20

The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169-1174) assumes a uniform distribution over the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. a. What are the average and spread of depth? b. What is the cdf of depth? c. What is the probability that observed depth is at most 10? Between 10 and 15? d. What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

asked 2021-08-03
Create equations to represent a relationship between quantities.
Define appropriate quantities for . . . descriptive modeling
Marcie can assemble 1 puzzle in 2 hours, and Janice can assemble 2 puzzles in 5 hours. How many hours will it take Marcie and Janice to assemble a puzzle if they work together?
asked 2021-10-26
A standard 3 sigma x-bar chart has been enhanced with early warning limits at plus-minus one sigma from the centerline . Three sample means in a row have plotted above the +1 sigma line . what is the probability of this happening if the process is still in control.
asked 2020-12-28

The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city. Population (thousands)WalkingSpeed (feet per second)5.50.6141.0711.61381.93422.2

New questions