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statistics principles and methods

Questions and Answers of Statistics Principles And Methods

=+6. Carry out the model utility test (H0: b 5 0). Explain
=+with the same standard deviation as for female students with no siblings, and so on? Discuss this with your partner, and then write a few sentences of explanation.
=+5. For the population of all female students at the university, do you think it is reasonable to assume that the distribution of heights at each particular x value is approximately normal and
=+4. Is the slope of the least-squares regression line from Step 3 equal to 0? Does this necessarily mean that there is a meaningful relationship between height and number of siblings in the
=+3. What is the equation of the least-squares line for these data?
=+2. Compute the value of the correlation coefficient. Is the value of the correlation coefficient consistent with your answer from Step 1? Explain.
=+1. Construct a scatterplot of the given data. Does there appear to be a linear relationship between y 5 height and x 5 number of siblings?Height Number of Height Number of(y) Siblings (x) (y)
=+Consider the following data on height (in inches) and number of siblings for a random sample of 10 female students at a large university.
=+In this activity, you should work with a partner (or in a small group).
=+■ If a correlation coefficient is reported, is it accompanied by a test of significance?Are the results of the test interpreted properly?
=+■ Has the model been used in an appropriate way? Has the regression equation been used to predict y for values of the independent variable that are outside the range of the data?
=+■ Does the model appear to be useful? Are the results of a model utility test reported? What is the P-value associated with the test?
=+■ If sample data have been used to estimate the coefficients in a simple linear regression model, is it reasonable to think that the basic assumptions required for inference are met?
=+■ Which variable is the dependent variable? Is it a numerical (rather than a qualitative) variable?
=+13.57 A sample of n 5 10,000 (x, y) pairs resulted in r 5.022. Test H0: r 5 0 versus Ha: r Þ 0 at significance level.05. Is the result statistically significant? Comment on the practical
=+b. Does this small P-value indicate that there is a very strong linear relationship between x and y (a value of r that differs considerably from zero)? Explain.
=+a. What conclusion would be appropriate at level of significance .001?
=+13.56 A sample of n 5 500 (x, y) pairs was collected and a test of H0: r 5 0 versus Ha: r Þ 0 was carried out. The resulting P-value was computed to be .00032.
=+Using a significance level of .05, determine whether the data support the hypothesis of a linear relationship between surface and subsurface concentration.
=+13.55 ● In a study of bacterial concentration in surface and subsurface water (“Pb and Bacteria in a Surface Microlayer” Journal of Marine Research [1982]: 1200–1206), the accompanying data
=+b. What proportion of observed variation in luminance can be attributed to the approximate linear relationship between luminance and particulate pollution?
=+a. Test to see whether there is a positive correlation between particulate pollution and luminance in the population from which the data were selected.
=+13.54 The accompanying summary quantities for x 5 particulate pollution (mg/m3) and y 5 luminance (.01 cd/m2)were calculated from a representative sample of data that appeared in the article
=+b. If y were regressed on x, would the regression explain a substantial percentage of the observed variation in grade point average? Explain your reasoning.
=+a. Does this suggest that there is a negative correlation between these two variables in the population from which the 528 students were selected? Use a test with significance level .01.
=+13.53 Television is regarded by many as a prime culprit for the difficulty many students have in performing well in school. The article “The Impact of Athletics, Part-Time Employment, and Other
=+13.50 If the sample correlation coefficient is equal to 1, is it necessarily true that r 5 1? If r 5 1, is it necessarily true that r 5 1?
=+13.49 Discuss the difference between r and r.
=+which has a t distribution based on (n 2 2) df when H0 is true, to test the hypotheses at significance level .01.
=+Suppose that the system is actually a prototype model, and the manufacturer does not wish to produce this model unless the data strongly indicate that when maximum outdoor temperature is 828F, the
=+13.48 ● The article “Performance Test Conducted for a Gas Air-Conditioning System” (American Society of Heating, Refrigerating, and Air Conditioning Engineering[1969]: 54) reported the
=+what can be said about the simultaneous prediction level?
=+b. If three different 99% prediction intervals are calculated for distances (cm) of 35, 40, and 45, respectively,
=+when distance is 45 cm, so that the simultaneous prediction level is at least 90%.
=+a. Return to Exercise 13.46 and obtain prediction intervals for sunburn index both when distance is 35 cm and
=+13.47 By analogy with the discussion in Exercise 13.46, when two different prediction intervals are computed, each at the 95% prediction level, the simultaneous prediction level is at least [100 2
=+e. Return to Part (d) and answer the question posed there if the individual confidence level for each interval were 99%.
=+when x 5 45, what do you think would be the simultaneous confidence level for the three resulting intervals?
=+d. If a 95% confidence interval were computed for the true mean index when x 5 35, another 95% confidence interval were computed when x 5 40, and yet another one
=+c. If two 99% intervals were computed, what do you think could be said about the simultaneous confidence level?
=+Calculate confidence intervals for the true mean sunburn index when the distance is 35 cm and when the distance is 45 cm in such a way that the simultaneous confidence level is at least 90%.
=+b. When two 95% confidence intervals are computed, it can be shown that the simultaneous confidence level is at least [100 2 2(5)]% 5 90%. That is, if both intervals are computed for a first
=+a. Calculate a 95% confidence interval for the true average sunburn index when the distance from the light source is 35 cm.
=+13.46 A regression of y 5 sunburn index for a pea plant on x 5 distance from an ultraviolet light source was considered in Exercise 13.22. The data and summary statistics presented there give a x
=+d. Explain the difference in interpretation of the intervals computed in Parts (b) and (c).
=+c. Construct a 90% prediction interval for the blood-lead level of a particular person who works where the air-lead level is 100 mg/m3.
=+b. Estimate the mean blood-lead level for people who work where the air-lead level is 100 mg/m3 using a 90%interval.
=+a. Find the equation of the estimated regression line.
=+13.45 High blood-lead levels are associated with a number of different health problems. The article “A Study of the Relationship between Blood Lead Levels and Occupational Lead Levels”
=+13.44 For the cereal data of Exercise 13.43, the average x value is 19.21. Would a 95% confidence interval with x* 5 20 or x* 5 17 be wider? Explain. Answer the same question for a prediction
=+d. According to the article, taste tests indicate that this brand of cereal is unacceptably soggy when the moisture content exceeds 4.1. Based on your interval in Part (c), do you think that a box
=+c. Find a 95% interval for the moisture content of an individual box of cereal that has been on the shelf 30 days.
=+b. Does the simple linear regression model provide useful information for predicting moisture content from knowledge of shelf time?
=+a. Summary quantities are Find the equation of the estimated regression line for predicting moisture content from time on the shelf.
=+are from “Computer Simulation Speeds Shelf Life Assessments” (Package Engineering [1983]: 72–73).x 0 3 6 8 10 13 16 y 2.8 3.0 3.1 3.2 3.4 3.4 3.5 x 20 24 27 30 34 37 41 y 3.1 3.8 4.0 4.1 4.3
=+13.43 ● The shelf life of packaged food depends on many factors. Dry cereal is considered to be a moisture-sensitive product (no one likes soggy cereal!) with the shelf life determined primarily
=+d. Calculate a 95% prediction interval for the maximum width of a food package with a minimum width of 6 cm.
=+c. Calculate a 95% confidence interval for the mean maximum width of products with a minimum width of 6 cm.
=+b. Calculate and interpret se.
=+a. Use the information given there to test the hypothesis that there is a positive linear relationship between the minimum width and the maximum width of an object.
=+13.42 The article first introduced in Exercise 13.28 of Section 13.3 gave data on the dimensions of 27 representative food products.
=+e. Predict the clutch size for a salamander with snout-vent length of 105.
=+d. Predict the clutch size for a salamander with a snoutvent length of 65 using a 95% interval.
=+c. Is there sufficient evidence to conclude that the slope of the population line is positive.
=+b. Calculate the standard deviation of b.
=+a. What is the equation of the regression line for predicting clutch size based on snout-vent length?
=+The regression equation is Y = –133 + 5.92x Predictor Coef StDev T P Constant 133.02 64.30 2.07 0.061 x 5.919 1.127 5.25 0.000 s = 33.90 R-Sq = 69.7% R-Sq(adj) = 67.2%Additional summary
=+Clutch Size 45 215 160 170 190 Snout-Vent Length 57 57 58 58 59 Clutch Size 200 270 175 245 215 Snout-Vent Length 63 63 64 67 Clutch Size 170 240 245 280 sa1b12002
=+13.41 ● According to “Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana”(Journal of Herpetology [1999]: 100–105), the size of a female salamander’s snout is
=+e. MINITAB gave (8.147, 10.065) as a 95% confidence interval for true average time when depth 5 300. Calculate a 99% confidence interval for this average.
=+d. A single observation on time is to be made when drilling starts at a depth of 200 ft. Use a 95% prediction interval to predict the resulting value of time.
=+c. MINITAB reported that 5 .347. Calculate a confidence interval at the 95% confidence level for the true average time when depth 5 200 ft.
=+b. Does the simple linear regression model appear to be useful?
=+a. What proportion of observed variation in time can be explained by the simple linear regression model?
=+s = 1.432 R-sq = 63.0% R-sq(adj) = 60.5%Analysis of Variance Source DF SS MS F p Regression 1 52.378 52.378 25.54 0.000 Error 15 30.768 2.051 Total 16 83.146
=+13.40 An experiment was carried out by geologists to see how the time necessary to drill a distance of 5 ft in rock(y, in min) depended on the depth at which the drilling began (x, in ft, between 0
=+(b)? Answer without calculating the interval.
=+c. When the milk temperature is 608C, would a 99% prediction interval be wider than the intervals of Parts (a) and
=+b. Calculate a 99% prediction interval for a single pH observation when milk temperature 5 358C.
=+a. Obtain a 95% prediction interval for a single pH observation to be made when milk temperature 5 408C.
=+c. Would you recommend using the data to calculate a 95% confidence interval for the true average pH when the temperature is 908C? Why or why not?13.39 Return to the regression of y 5 milk pH on x
=+b. Calculate a 99% confidence interval for the true average milk pH when the milk temperature is 358C.
=+true average milk pH when the milk temperature is 408C.
=+using a 95% confidence level for the mean vote difference proportion for congressional races where 60% judge candidate A as more competent.13.38 The data of Exercise 13.25, in which x 5 milk
=+13.37 Example 13.3 gave data on x 5 proportion who judged candidate A as more competent and y 5 vote difference proportion. Calculate a confidence interval sa1b12.02 x
=+d. For what value x* is the estimated standard deviation of a 1 bx* smallest, and why?
=+c. Calculate the estimated standard deviation of the statistic a 1 b(2.8).
=+a. Calculate the estimated standard deviation of the statistic a 1 b(2.0).b. Without any further calculation, what is sa1b(3.0) and what reasoning did you use to obtain it?
=+13.34 Explain the difference between a confidence interval and a prediction interval. How can a prediction level of 95% be interpreted?13.3 are a tell f is fo 13.3 y 5 oxygen consumption on x 5
=+casts doubt on the appropriateness of the simple linear regression model? Explain.Year 1963 1964 1965 1966 1967 1968 x 188.5 191.3 193.8 195.9 197.9 199.9 y 2.26 2.60 2.78 3.24 3.80 4.47 Year 1969
=+13.33 ● The accompanying data on x 5 U.S. population(millions) and y 5 crime index (millions) appeared in the article “The Normal Distribution of Crime” (Journal of Police Science and
=+b. Construct a standardized residual plot. Does the plot differ significantly in general appearance from the plot in Part (a)?
=+yˆx 17.0 17.0 24.3 24.3 24.3 y 539 728 945 738 759 Residual 255.7 133.3 107.2 299.8 278.8 St. resid. 20.63 1.51 1.35 21.25 20.99a. Plot the (x, residual) pairs. Does the resulting plot suggest
=+13.32 ● An investigation of the relationship between traffic flow x (thousands of cars per 24 hr) and lead content y of bark on trees near the highway (mg/g dry weight)yielded the accompanying
=+c. Based on your plot in Part (a), do you think that it is reasonable to assume that the variance of y is the same at each x value? Explain.
=+b. Is there any pattern in the standardized residual plot that would indicate that the simple linear regression model is not appropriate?
=+a. Construct a standardized residual plot. Are there any unusually large residuals? Do you think that there are any influential observations?
=+x 164.2 156.9 109.8 111.4 87.0 y 181 156 115 132 96 St. resid. 2.52 0.82 0.27 1.64 0.08 x 161.8 230.9 106.5 97.6 79.7 y 170 193 110 94 77 St. resid. 1.72 20.73 0.05 20.77 21.11 x 118.7 248.8 102.4
=+Optical Carbon Analysis Methods: Application to Diesel Vehicle Exhaust Aerosol” Environmental Science Technology [1984]: 231–234). The estimated regression line for this data set is 5 31 1
=+13.31 ● ▼ Carbon aerosols have been identified as a contributing factor in a number of air quality problems. In a chemical analysis of diesel engine exhaust, x 5 mass(mg/cm2) and y 5 elemental

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