Researchers at a science corporation and a university collaborated on a study of how air traffic controllers respond to false alarms. The researchers theorize that the high rate of false alarms regarding mid-air collisions leads to the "cry wolf" effect (the tendency for air traffic controllers to ignore true alerts in the future). The investigation examined data on a random sample of 445 conflict alerts. Each alert was first classified as a "true" or "false" alert. Then, each was classified according to whether or not there was a human controller response to the alert. A summary of the responses is provided in the accompanying table. Do the data indicate that the response rate of air traffic controllers to mid-air collision alarms differs for true and false alerts? Test using ? = 0.01. What inference can you make concerning the "cry wolf" effect? Contingency Table Specify the null and alternative hypotheses. Choose the correct answer below. A. H0: The classifications Alert and Response are independent. Ha: The classifications Alert and Response are dependent. B. H0: The classifications No Response and Response are independent. Ha: The classifications No Response and Response are dependent. C. H0: The classifications Alert and Response are dependent. Ha: The classifications Alert and Response are independent. D. H0: The classifications True alert and False alert are independent. Ha: The classifications True alert and False alert are dependent. Find the test statistic. ?² = __ (Round to two decimal places as needed.) Determine the p-value. p-value = __ (Round to three decimal places as needed.) State the conclusion. Reject H0. There is insufficient evidence to indicate the two classifications are independent at ? = 0.01. No Response Response Totals True alert 6 233 239 False alert 32 174 206 Totals 38 407 445
Added by Steven C.
Close
Step 1
Null hypothesis (H0): There is no cry wolf effect, and the response rate of air traffic controllers to mid-air collision alarms is the same for true and false alerts. Alternative hypothesis (Ha): There is evidence of the cry wolf effect, and the response rate of Show more…
Show all steps
Your feedback will help us improve your experience
Ivan Kochetkov and 61 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Researchers at Alion Science Corporation and New Mexico State University collaborated on a study of how air traffic controllers respond to false alarms (Human Factors , Aug. 2009). The researchers theorize that the high rate of false alarms regarding midair collisions leads to the "cry wolf" effect, i.e., the tendency for air traffic controllers to ignore true alerts in the future. The investigation examined data on a random sample of 437 conflict alerts. Each alert was first classified as a "true" or "false" alert. Then, each was classified according to whether or not there was a human controller response to the alert. The number of the 437 alerts that fall into each of the combined categories is given as follows: True alert/No response-3; True alert/ Response-231; False alert/No response-37; False alert/ Response-166. This summary information is saved in the ATC file. Do the data indicate that the response rate of air traffic controllers to midair collision alarms differs for true and false alerts? Test using a = .05. What inference can you make concerning the "cry wolf" effect?
Madhur L.
Wolf packs tend to be large extended family groups that have a well-defined hunting territory. Wolves not in the pack are driven out of the territory or killed. In ecologically similar regions, is the size of an extended wolf pack related to the size of the hunting region? Using radio collars on wolves, the size of the hunting region can be estimated for a given pack of wolves. Let x represent the number of wolves in an extended pack and y represent the size of the hunting region in km²/1000. The following data are representative of one of the national parks. x wolves 29 31 22 67 96 y km²/1000 7.37 12.14 8.17 15.36 16.85 (a) Verify that Σx = 245, Σy = 59.89, Σx² = 15,991, Σy² = 788.2975, Σxy = 3416.53, and r ≈ 0.9063. (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0. Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. (c) Verify that Se ≈ 2.0550, a ≈ 6.0537, and b ≈ 0.12090. (d) Find the predicted size of the hunting region for an extended pack of 56 wolves. (Use 2 decimal places.) km²/1000 (e) Find an 85% confidence interval for your prediction of part (d). (Use 1 decimal place.) lower limit km²/1000 upper limit km²/1000 (f) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0. Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is sufficient evidence that β > 0. (g) Find a 95% confidence interval for β and interpret its meaning in terms of drift rate. (Use 2 decimal places.) lower limit upper limit Interpretation For every wolf joining the pack, the hunting territory decreases by an amount that falls within the confidence interval. For every wolf joining the pack, the hunting territory increases by an amount that falls within the confidence interval. For every wolf joining the pack, the hunting territory decreases by an amount that falls outside the confidence interval. For every wolf joining the pack, the hunting territory increases by an amount that falls outside the confidence interval.
Rachel G.
In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups:Group $1,$ the simple group, required to respond as quickly as possible after a stimulus was presented; Group $2,$ the go/no-go group, required to respond to a particular stimulus while disregarding other stimuli; and Group $3,$ the choice group, required to respond differently depending on the type of whistle sound, the subject must press a certain button. The researcher wants to determine if the mean reaction times for each stimulus are equal. The reaction time (in seconds) for each stimulus is presented in the table. $$\begin{array}{lcc}\text { Simple } & \text { Go/No-Go } & \text { Choice } \\\hline 0.430 & 0.588 & 0.561 \\\hline 0.498 & 0.375 & 0.498 \\\hline 0.480 & 0.409 & 0.519 \\\hline 0.376 & 0.613 & 0.538 \\\hline 0.402 & 0.481 & 0.464 \\\hline 0.329 & 0.355 & 0.625\end{array}$$ (a) What type of experimental design is this? (b) What is the response variable? What is the explanatory variable? How many levels of treatment are there in this experiment? (c) State the null and alternative hypotheses. (d) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from a normal population. (e) Test the hypothesis that the mean reaction times for the three stimuli are the same at the $\alpha=0.05$ level of significance. (f) Draw boxplots of the three stimuli to support the analytic results obtained in part (c).
Comparing Three or More Means
Comparing Three or More Means (One-Way Analysis of Variance)
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD