Concept explainers
(a) Suppose that a study of coho salmon suggests the population model
Where
(b) Find a value of an initial population
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardUrban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forward
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardQuestion 12: Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 68% . He examines a random sample of 500 emails received at an email server, and finds that 361 of the messages are spam. Can you conclude that the percentage of emails that are spam is greater than 68%? Use both a=0.10 and a=0.01 levels of significance and the P-value method with the TI-84 Plus calculator. Part 1: State the appropriate null and alternate hypotheses. H0: H1: This hypothesis test is a (BLANK) test. Part 2: Compute the value of the test statistic. Round the answer to at least two decimal places. z=(BLANK) Part 3: Compute the P-value. Round the answer to at least four decimal places. P-value: (BLANK) Part 4: (d) Determine whether to reject H0. At the a=0.10 level, ▼(Choose one) the null hypothesis H0. At the a=0.01 level, ▼(Choose one) the null hypothesis H0. Part 5:…arrow_forwardPopulation of Females Under 18 Using projected data from 2020 to 2060, the population offemales under 18 in the United States is given byy = 154.03x + 34,319, with x equal to the numberof years after 2000 and y equal to the projected population, in thousands. In what year will the populationreach 38,169,750, according to this model?(Source: U.S. Census Bureau)arrow_forward
- The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows. Catfish Bass Bluegill Pike 122 75 222 81 In the 5-year interval, did the distribution of fish change at the 0.05 level Find the value of the chi-square statistic for the sample. Estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005 Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the…arrow_forwardPi- P2 Z. = %3D SE Suppose a drug company is developing a vaccine, designed to protect against a particular virus. The company states that the vaccine will be equally effective for men and women. In its initial stage, a researcher selects a random sample of 200 men and 100 women independently. At the end of the study, 15 of the men and 10 of the women showed symptoms of the virus after taking the vaccine. Is there enough evidence to conclude that there is a significant difference in the proportions of men and women who show symptoms of the virus after taking the vaccine? (a) State the appropriate hypotheses to answer this question. (b) Compute the test-statistic. (c) (i) Calculate the p-value. (ii) Interpret the p-value you have found. (d) State your conclusion in context of the situation. Page 1 135arrow_forwardquestion 8arrow_forward
- Lecture(8.1): A research study was conducted that measured empathy after watching Sesame street for five days in a row. The study was conducted twice. For Study A the researcher recruited 20 children and randomly assigned them into 2 groups, one group who watched Sesame street. and a second group who did not watched Sesame street. Empathy was measured after 5 days. For study B the researcher decided to only recruit only 10 children who all watched Sesame street and this time measued empathy before the first hour of Sesame street and again afte 5 days once the lasr hour was watched. Which of these studies uses an independent sample and which uses a dependent sample.?arrow_forwardQ.7arrow_forwardWage B1 B2 educ + €, where = 1. Wage means daily wage measured in dollars. 2. educ means years of education (schooling) The regression output is given below: reg wage educ Source | SS df MS Number of obs = 100 F(2, 97) = 97.14 Model 10000.00 1 5000.00 Prob > F = 0.0000 Residual | 10000.00 98 100.00 R-squared = 0.5000 Adj R-squared = 0.4900 Total | 20000.00 99 200.00 Root MSE = 10.000 wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] educ | 10.0000 _cons | 10.0000 5.0000 10.0000 2.00 0.050 0.0000 20.0000 1.00 0.317 -20.0000 30.0000arrow_forward
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