8 Julia is waiting for either of the two buses to her destination, and waiting times for those two different buses follow independent exponential distributions with mean 3 minutes and 7 minutes. Assuming she would get on the bus that comes first, what is her expected waiting time?
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- One tree in the study had a weight that exceeded its expected weight (according to the best fit curve) by more than that of any other tree. By how many tons did the trees actual weight exceed the expected weight for its height?Suppose you are interested in the role of social support in immune function among retired men who live alone. You ask 50 patients to record the number of days they do not see or interact with a friend or family member over a period of 1 month to see whether the number of nonsocial days in a typical month correlates with the number of new illnesses they experience per year. You decide to use the computational formula to calculate the Pearson correlation between the number of nonsocial days in a month and the number of illnesses per year. To do so, you call the number of nonsocial days in a month X and the number of illnesses per year Y. Then, you add up your data values (∑X and ∑Y), add up the squares of your data values (∑X2 and ∑Y2), and add up the products of your data values (∑XY). The following table summarizes your results: ∑X 590 ∑Y 380 ∑XY 4,887 ∑X2 10,456 ∑Y2 4,258 Find the following values: The sum of squares for the number of nonsocial days in a month is SSX=…The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.01 level of significance. Swimmers at the City Pool Monday Tuesday Wednesday Thursday Friday Number 64 46 41 56 70 Copy Data Step 2 of 4 : Calculate the expected value for the number of swimmers on Tuesday. Enter your answer as a fraction or a decimal rounded to three decimal places.
- 9The Baytown Post Office has 4 stations for service. Customers line up in single file for service on an FIFO basis. The mean arrival rate is 32 per hour, Poison distributed, and the mean service time per server is 6 minutes, exponentially distributed. Compute the operating characteristics for this operation. Does the operation appear to be satisfactory in terms of: (a) Postal workers' (servers') idle time; (Round answer to 3 decimal places, e.g. 2.750.) (b) customer waiting time and the number waiting for service; (c) the percentage of the time a customer can walk in and get served without waiting at all?11. In this same article on sleep duration and start time, researchers also considered whether school start time was related to obtaining an adequate amount of sleep. An adequate amountbof sleep was considered at least 8.5 hours of sleep, as recommended by the National Sleep Foundation. The authors used logistic regression models to associate the probability of adequate sleep to school start time. Here are some adapted logistic regression results from this study: In(odds of adequate sleep) = 6, + B,, where x1 = school start time, measured as the number of minutes after 7 AM that the school starts. For this model, B,-0.014, SE(B,)-0.005. - What Is the estimated odds ratlo of adequate sleep, and 95% CI, for students who start at 8:30 AM compared to those who start at 7:30 AM? a. 1.01 (1.00, 1.02) b. 1.52 (1.13, 2.05) C. 2.32 (1.27, 4.22) d. 4.05 (1.49, 11.02)
- Q5: The theory that resistance by mosquitoes to an insecticide is due to a single dominant gene has been examined. Homozygous resistant mosquitoes were crossed with homozygous susceptible mosquitoes to give A heterozygous population. These were crossed to the homozygous susceptible population. Of this back cross progeny 465 were exposed to the insecticide, 264 died. Is the percentage killed significantly different to the percentage predicted by the model?2. I surveyed 150 adults in the U.S. and asked them how many hours of TV the watched on average per week. I then ran a regression of # of hours of TV on whether or not they were a college graduate (=1 if yes, =0 if no), their age in years, the number of children in their household, and whether or not they live a cold climate (=1 if latitude is greater than 41.2, =0 otherwise). The results fro the regression are shown in the table below. Estimate p-value College Graduate -0.8 0.003 Age 0.1 0.150 Number of Children 0.10 0.521 Cold Climate 1.8 0.047 Intercept -1.23 0.041 (a) What is the dependent variable in this regression? (b) What are the independent variable(s) in this regression? (c) What is the unit of analysis? (d) What is the sample size? (e) What is one binary variable used in this analysis? (f) What is one ratio variable used in this analysis? (g) What is the predicted number of TV hours watched by a 50 year old, colleg graduate, with no children at home who lives in Arizona…t has been suggested that gossiping about others may affect how likeable you are. Two groups of participants are asked to read a vignette describing a fictional person. They are then asked to rate how much they would like the person described in the vignette on a continuous scale from 1-15, where higher scores represent a higher likability. The first group of participants (n=20) reads a vignette describing a person that frequently gossips and obtains an average likability score of (M1) with a variance of (S12). The second group of different participants (n=20) reads a vignette describing a person that never gossips and obtains an average likability score of (M2) with a variance of (S22). Given that there is not much research in this area, test the hypothesis that gossiping impacts likability at an alpha=0.05. 1, Are the results you obtained meaningful? report the results here for your effect size showing all your work and your interpretation 2. Report the results of the study…
- 4. As fallen trees lie on the forest floor they slowly decay. Will the amount of light present have an impact on the rate of decay? In the following table x is a random variable representing the remaining percentage of total mass of a log after it was exposed to the elements for three weeks while y represents the numbers of hours of direct sunlight the log received each day. X 0.60 .70 .65 .82 .87 y 1.0 2.3 3.0 4.0 4.5 (a) Plot a scatter diagram of the data. Remember to label your axes appropriately and choose a consistent scale. (b) Based on a scatter diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative? Please circle one of the following choices: A. Positive B. Close to zero C. Negative (c) Interpret your results from parts (a) and (b). 16 tvSuppose you are fitting a survival model and the outcome of interest is time to the diagnosis of cancer (T). A subject entered the study at t=0 and the diagnosis of cancer did not occur by the end of the study period, what kind of event is that? It is an interval-censored observation because an event happened between time of entry and the exit. It is a right-censored observation because no event will be observed during the study period. It is a left-censored observation where the event of interest happened before the study starts. It is a right-censored observation because the event has already occurred.According to a JHU study published in the American Journal of Public Health, widows live longer than widowers. Consider the following survival data collected on 100 widows and 100 widowers following the death of spouse: Years Lived Widow Widower Less than 5 25 39 5 to 10 42 40 More Than 10 33 21 Can we conclude at 0.05 level of significance that the proportions of widows and widowers are equal with respect to the different time periods that a spouse survives after the death of his or her mate?