Exam 12: Statistical Analysis Questions in ANOVA and Rank-Sum Test

Use the given set of points to compute the residual standard deviation $s _ { \mathrm { e } }$ x 13 10 10 11 13 7 11 6 y 32 26 23 24 28 16 26 21

Use the given set of points to construct a 95 % confidence interval for the mean response for the given value of x x 20 13 12 10 11 10 y 108 69 63 55 58 53 xequals12

In a study of reaction times,) The regression equation is Auditory $= 181.501124 + 0.408378$ Visual Predictor Coef SE Coef T P Constant 181.501124 21.861296 8.302395 0.00115 Visual 0.408378 0.113544 3.596642 0.022827 What is the slope of the least-squares regression line?

A biology professor claims that,) Grade 1 2 3 4 5 Observed 26 34 50 4 13 Compute the expected frequencies.

The following data was collected as part of a study examining whether there is a difference between the number of hours men and women watch television. The values represent the number of hours a subject watched television on a designated Tuesday night. Lower values rank ahead of higher ones. Men 2.0 1.5 3.0 2.5 2.0 1.0 0.0 2.0 1.5 2.5 2.0 2.0 Women 2.0 2.5 1.0 1.0 1.5 2.5 2.0 1.0 2.0 1.5 1.0 0.0 a) Calculate the $P$ -value. b) Can you conclude that the median times watching television are different? Use the $\alpha = 0.10$ level of significance.

Construct the multiple regression sequence $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 }$ for the following data set: y 31.3 50 19 4.0 56.9 90 38 8.0 43.1 70 28 6.5 41.5 70 25 5.5 39.0 60 26 6.5 40.9 70 29 5.0 35.9 60 23 5.5 43.5 70 28 5.5 47.9 80 34 6.5 33.8 70 26 4.5

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 5 , n _ { 2 } = 6$ and $n _ { 3 } = 5$ The sample means were $\bar { x } _ { 1 } = 1.95 , \bar { x } _ { 2 } = 1.73 , \text { and } \bar { x } _ { 3 } = 1.44 \text {. }$ The sample standard deviations were $s _ { 1 } = 0.28 , s _ { 2 } = 0.43 , \text { and } s _ { 3 } = 0.48$ The grand mean is $\overline { \bar { x } } = 1.708125$ How many degrees of freedom are there for SSE.

For the following data, compute the test statistic and the critical value, and determine whether to reject $H _ { 0 }$ at the $\alpha = 0.10$ level. Sample A 42 55 59 57 49 60 43 54 Sample B 28 44 42 64 61 46 39 63

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines What is the $P$ -value?

The following MINITAB output presents a 99% confidence interval for the mean ozone Predicted Values for New Observations New Obs Fit SE Fit 99.0\% CI 99.0\% PI 1 35.73 1.3 (32.38,39.08) (19.47,51.99) Values of Predictors for New Observations New OBS Humidity 1 65.0\% What is the point estimate for the mean ozone level for days when the relative humidity is $65 \%$ ?

Find the $\alpha = 0.01$ critical value for the chi-square statistic with 14 degrees of freedom.

A sample of 149 university students who recently moved off-campus were polled to see whether 1 2 3 Agree 25 17 34 No Opinion 8 12 15 Disagree 11 18 6 Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether the mean fill volumes differ among the filling machines. What is the value of MSTr?

Use the given set of points to compute the predicted value $\hat { y }$ for the given value of x . x 13 14 16 13 13 16 y 61 66 75 60 64 72 x=12

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content. Can the mean effect of the rubber content be interpreted? If so, interpret the main effect. I $\alpha = 0.01$ level of significance.

The number of visits to a certain web site were counted each day of a particular week.

The following MINITAB output presents a multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } +$ $b _ { 2 } x _ { 2 } + b _ { 3 } x _ { 3 } + b _ { 4 } x _ { 4 }$ The regression equation is $\mathrm { Y } = 2.5919 - 1.3391 \mathrm { X } 1 + 0.6212 \mathrm { X } 2 + 1.6435 \mathrm { X } 3 + 1.4269 \mathrm { X } 4$ Predictor Coef SE Coef T P Constant 2.5919 0.6269 1.1668 0.337 X1 -1.3391 0.6716 3.5190 0.002 X2 0.6212 0.8488 -3.2848 0.004 X3 1.6435 0.7934 1.8821 0.090 X4 1.4269 0.7679 -0.9879 0.345 $\mathrm{S}=2.8912 \quad \mathrm{R}-\mathrm{Sq}=55.3 \% \mathrm{R}-\mathrm{Sq}(\mathrm{adj})=46.4 \%$ Analysis of Variance Source DF SS MS F P Regression 4 735.9 184.0 7.7311 0.003 Residual Error 25 594.6 23.8 Total 29 1330.5 Let $\beta _ { 3 }$ be the coefficient $X 3$ Test the hypothesis $H _ { 0 } : \beta _ { 3 } = 0$ versus $H _ { 1 } : \beta 3 \neq 0$ at the $\alpha = 0.05 \text { level. }$ What do you conclude?

Use the given set of points to compute the standard error of $b _ { 1 } , s _ { \mathrm { b } }$ x 7 7 10 8 14 8 5 9 y 16 18 21 16 33 19 17 23

Following are observed frequencies. The null hypothesis is $H _ { 0 } : p _ { 1 } = 0.35 , p _ { 2 } = 0.25$ $p _ { 3 } = 0.2 , p _ { 4 } = 0.1 , p _ { 5 } = 0.1$ Category 1 2 3 4 5 Observed 49 34 14 9 10 Test the hypothesis that the distribution of the observed frequencies is as given by the nul hypothesis. Use the $\alpha = 0.05$ level of significance.

In a study of reaction times,) Visual Auditory 185 244 204 244 242 247 209 245 191 243 250 249 155 237 188 245 Compute a point estimate for the mean auditory response time for subjects with a visual response time of 231.