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- Further Verification of Newtons Second LawThis exercise represents a hypothetical implementation of the experiment suggested in the solution of part 6 of Example 3.7. A mass of 15 kilograms was subjected to varying accelerations, and the resulting force was measured. In the following table, acceleration is in meters per second per second, and force is in newton. Acceleration Force 8 120 11 165 14 210 17 255 20 300 a. Construct a table of differences and explain how it shows that these data are linear. b. Find a linear model for the data. c. Explain in practical terms what the slope of this linear model is. d. Express, using functional notation, the force resulting from an acceleration of 15 meters per second per second, and then calculate that value. e. Explain how this experiment provides further evidence for Newtons second law of motion.2. Who supports gun control laws more: females or males? Data were collected from a sample of 980people. We see that 379 of the 460 females in the sample support gun control laws, while 318 of the520 males in the sample support gun control laws. We will investigate the difference in proportionsof females and males who support gun control laws.(This dataset is preloaded in StatKey.) a) What parameter are we trying to estimate? Give correct notation and a brief writtendescription. b) What is the best point estimate for the difference in the proportions of gun control lawsupporters? Use correct notation and include the value. _______________________________ c) Find a 99% bootstrap confidence interval using the Percentile Method□ Include a screen shot of your StatKey output.99% CI: d) Find a 95% bootstrap confidence interval using the Standard Error Method (showcalculations based on bootstrap estimate of standard error as shown in graph from previousstep): 95% CI: e) Interpret the 95%…Elephants and hippos We removed humans from thescatterplot in Exercise 31 because our species was anoutlier in life expectancy. The resulting scatterplot showstwo points that now may be of concern. The point in theupper right corner of this scatterplot is for elephants, andthe other point at the far right is for hippos.a) By removing one of these points, we could makethe association appear to be stronger. Which point?Explain.b) Would the slope of the line increase or decrease?c) Should we just keep removing animals to increase thestrength of the model? Explain.d) If we remove elephants from the scatterplot, the slopeof the regression line becomes 11.6 days per year. Doyou think elephants were an influential point? Explain.
- The Coruro’s Burrow. The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600 meters. Zoologists S. Begall and M. Gallardo studied the characteristics of the burrow systems of the subterranean coruro in central Chile and published their findings in the paper “Spalacopus cyanus (Rodentia: Octodontidae): An Extremist in Tunnel Constructing and Food Storing among Subterranean Mammals” (Journal of Zoology, Vol. 251, pp. 53–60). A sample of 51 burrows had the depths, in centimeters (cm), presented on the WeissStats site. Use the technology of your choice to do the following. a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data. b. Based on your results from part (a), can you reasonably apply the t-interval procedure to the data? Explain your reasoning. c. Find and interpret a 90% confidence interval for the mean depth of all subterranean coruro burrows.Which of the following is/are true? a) scientists typically study samples because they are especially interested inthem b) scientists typically study populations because they are usually quite small c) scientists typically study samples because they are too lazy to collect population data d) scientists typically study samples because collecting entire populations is usually not feasible e) scientists often use statistics on samples to estimate parameters on populations f) statistical inference is the process of inferring about populations based on knowledge of samples g) if we had complete access to population data, then computing such things as means and medians would never have to be done h) t-tests, z-tests, ANOVA, regression, are all statistical procedures that help us make inferences about populations based on sample data i) b, d, e, f j) d, e, f, h k) all except cWhich of the following is/are true? a) scientists typically study samples because they are especially interested in them b) scientists typically study populations because they are usually quite small c) scientists typically study samples because they are too lazy to collect population data d) scientists typically study samples because collecting entire populations is usually not feasible e) scientists often use statistics on samples to estimate parameters on populations f) statistical inference is the process of inferring about populations based on knowledge of samples g) if we had complete access to population data, then computing such things as means and medians would never have to be done h) t-tests, z-tests, ANOVA, regression, are all statistical procedures that help us make inferences about populations based on sample data i) b, d, e, f j) d, e, f, h k) all except c
- A dietitian wants to test if on the average a person’s cholesterol level will be lowered if their diet is supplemented with a certain mineral. Six subjects have their cholesterol level tested before taking this mineral and again after taking this mineral for a 3 months. The measured cholesterol levels are listed in the table below: Level Before Mineral 210 235 208 190 172 244 Level After Mineral 190 170 210 188 173 228 When doing a Hypothesis Test to test this dietitian's claim the Degree of Freedom used and the computed P-value are A.) Degree of Freedom = 10 and P-value = 0.1349 B.) Degree of Freedom = 9.6562 and P-value = 0.1354 C.) Degree of Freedom = 5 and P-Value = 0.1688 D.) Degree of Freedom = 5 and P-value = 0.0844Imagine you would like to estimate the effect of the amount of rainfall in a given month in a region on the number of cars that were caught speeding in that region in a given month. You have data on both variables for multiple months. For this estimation, you can write down the error term of the econometric model as . a) What kind of factors are captured in ? Give a general explanation and one example of such a factor in the specific context described above. b) What kind of factors are captured in ? Give a general explanation and one example of such a factor in the specific context described above.1) Parking at a XYZ university has become a very big problem. University administrators are interested in determining the average parking time of its students. An administrator inconspicuously followed 220 students and carefully recorded their parking times. The average parking time for the 220 students was 17 minutes. Jane Doe, one of the 220 students, took 19 minutes to find a a parking spot. Identity the following for the scenario above: a) Population b) Sample c) Parameter d) Statistic e) Variable t) Data
- Salinity in Quebec river is a combination of tides and rain. Rain that diluted the salt occurs about 10% of the time, while the non salty outgoing tides occurs twice per day. You take your dog for a walk down by the river at random during the weekend and notice that he'll drink from the river 30% of the time when the salt is sufficiently low. someone points out that the saltiness doesn't depend on the local rain but on the rain upriver. Assume that at any time it is possible to have 3 independent rainstorms upriver , all with the same 10% probability of occurrence that you see at the city. What is the probability of no rain upriver ? Of 1 rain ? Of more than one ? please tell which probability formula you useA researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) say about the treatment a. The treatment causes a change in the scores. b. The treatment adds a constant to each score. c. The treatment multiplies each score by a constant. d. The treatment has no effect on the scores.Which of the following can be inferred from the figure above? Error Bars are Standard Errors. (Quality of content ratings, based on a sample of college students, is on the y-axis) Hulu and Disney+ don't have a significantly different quality of content Netflix has significantly higher quality content than Hulu HBO Max has higher quality content than all other services We cannot infer any of the above from the information given.