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A: Topic:- limit and continuity
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- Stock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentThe population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?An experiment is conducted to determine the relationship between the amount of a certain drug in the bloodstream and the length of time it takes to react to a stimulus. A random sample of 5 persons who took this drug is selected. The amount of drug in the bloodstream x and the reaction time y in selected persons showed thatAmount of drugs x: 2 1 4 3 5Reaction time y: 1 1 2 2 4Σx=15 , Σx² = 55, Σy=10, Σy² = 26, Σxy = 37 (c) Find the equation of the regression line between y and x. (d) Use the equation in part (c) to predict y when x=3.5. (e) Test whether the slope of the population regression line is positive against the default that it is zero is Ho B₁ = 0 vs H, B₁ > 0. Use a=0.05.
- A random sample of 1000 people with known allergies to poison ivy participated in a recent study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, the oil it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. Observed reactions were recorded as "none," "mild," or "strong." The results are summarized in the following table. Reaction Within 5 Minutes After 5 Minutes Row Total NoneMildStrong 4056530 48326126 453391156 Column Total 500 500 1000 Suppose a person selected at random from this sample of 1000 subjects. What is the probability that a strong reaction was observed, given that the oil was washed off within 5 minutes?Infants, even newborns, prefer to look at attractive faces compared to less attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s faces. Previously, a group of adults had rated one of the faces as significantly more attractive than the other. The babies were positioned in front of a screen on which the photographs were presented. The pair of faces remained on the screen until the baby accumulated a total of 20 seconds of looking at one or the other. The number of seconds looking at the attractive face was recorded for each infant. Suppose that the study used a sample of n = 9 infants and the data produced an average of M = 13 for the attractive face with an estimated standard error sM= 1 (SS = 72). If there were no preference, the 20 seconds should be divided equally between the two photographs. Note that all the available information comes from the sample. Specifically, we do not know the population mean or the…Infants, even newborns, prefer to look at attractive faces compared to less attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s faces. Previously, a group of adults had rated one of the faces as significantly more attractive than the other. The babies were positioned in front of a screen on which the photographs were presented. The pair of faces remained on the screen until the baby accumulated a total of 20 seconds of looking at one or the other. The number of seconds looking at the attractive face was recorded for each infant. Suppose that the study used a sample of n = 9 infants and the data produced an average of M = 13 for the attractive face with an estimated standard error sM= 1 (SS = 72). If there were no preference, the 20 seconds should be divided equally between the two photographs. Note that all the available information comes from the sample. Specifically, we do not know the population mean or the…
- An experiment is conducted to determine the relationship between the amount of a certain drug in the bloodstream and the length of time it takes to react to a stimulus. A random sample of 5 persons who took this drug is selected. The amount of drug in the bloodstream x and the reaction time y in selected persons showed that Amount of drugs x: 2 1 4 3 5 Reaction time y: 1 1 2 2 4 Σx=15 , Σx² = 55, Σy=10, Σy² = 26, Σxy = 37 (a) Compute SSxx, SSyy, and SSxy (b) Compute the correlation coefficient r and explain it in the context of the problem. (c) Find the equation of the regression line between y and x.18. please have all 6 steps of the p method listed clearly! Truck pollution: In an experiment to determine the effect of ambient temperature on the emissons of oxides of nitrogen ( NOx ) of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F . The emissions, in parts per billion, are presented in the following table. Truck 40°F 80°F 1 951.6 924.1 2 836.1 862.0 3 984.1 960.6 4 937.2 837.0 5 895.4 863.7 6 1018.2 970.0 7 944.5 838.5 8 843.9 784.8 9 837.8 857.9 10 967.4 913.9 Send data to Excel Let μ1 represent the mean emission at 40°F and =μd−μ1μ2 .Can you conclude that the mean emissions are higher at 40°F ? Use the =α0.05 level of significance and the TI-84 Plus calculator to answer the following.Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
- A researcher collects data that represents the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. The researcher is interested in whether the two groups reliably differ in the amount of sleep they get. Use Jamovi to calculate t-obt and the p value.Q1 When regressing number of crimes committed by an individual against years of education you omit the relevant variable innate ability. Then, the estimated coefficient for education is going to be: A downwards biased B. upwards biased C. biased, but we cannot say in which direction D. not biased Q2 You estimate the equation: Y=6.2+0.41X. After finding heteroscedasticity, you run a second equation: Y/X=0.39+6.31/X. What is the effects of X on Y based on your preferred specification? A. A 1 unit change in X increases Y by 6.31 units. B. A 1 unit change in X increases Y by 0.39 units C. A 1 unit change in X increases Y by 6.31%. D. A 1 unit change in X increases Y by 39% Q 3 Which of the following are advantages of the use of panel data over pure cross- sectional or pure timeseries modelling? (i) The use of panel data can increase the number of degrees of freedom and therefore the power of tests (ii) The use of panel data allows the average value of the dependent…For a hypothesis test of the claim that the mean amount of sleep for adults is less than 8 hours, technology output shows that the hypothesis test has power of 0.4574 of supporting the claim that u < 8 hours of sleep when the actual population mean is 7.5 hours of sleep. Interpret this value of the power, then identify the value of beta and, interpret that value.
