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

What is the margin of error? The summary statistics for a certain set of points are: $n = 18 , s _ { \mathrm { e } } = 2.127$ , $\sum ( x - \bar { x } ) ^ { 2 } = 13.384$ , and $b _ { 1 } = 1.376$ . Assume the conditions of the linear model hold. A $95 \%$ confidence interval for $\beta _ { 1 }$ will be constructed.

For the given table of observed frequencies:

Use the given set of points to compute the sum of squares for x , $\sum ( x - \bar { x } ) ^ { 2 }$ x 5 9 10 7 7 10 6 8 y 16 22 27 20 21 22 20 21

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below Can you reject the hypothesis of no interactions?

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis $H_{0}: \beta_{1}=0$ . Can you conclude that the explanatory variable is useful in predicting the outcome variab Answer this question using the $\alpha = 0.05$ level of significance.

In a study of reaction times,) Visual Auditory 166 241 192 242 242 250 188 244 232 252 240 254 197 245 203 247 Predict the auditory response time for a particular subject whose visual response time of 178.

The length of time that customers spent eating dinner was compared with and without music playing. The times, in minutes, were as follows Without Music 51 68 55 51 40 70 41 57 85 59 60 47 With Music 73 80 60 73 44 81 87 75 94 40 89 63 92 78 66 a) Compute the $P$ -value. b) Can you conclude that the median times eating dinner differ with and without music? I $= 0.01$ level of significance.

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 you reject the hypothesis of no interactions?

The following table shows the weekly total sales (in dollars) at a small roadside vegetable stand for the months June through September. Month Weekly Sales June 1132 791 1006 990 July 1060 1069 1007 1093 August 1181 1143 1248 1223 September 841 855 957 943 Perform a Tukey-Kramer test to determine which pairs of means, if any, differ. Use the $\alpha$ level of significance.

In a study of reaction times,) Visual Auditory 208 200 177 175 250 233 248 234 152 155 164 161 196 190 238 230 Compute the least-squares regression line for predicting auditory response time $( y )$ from visual response time $( x )$ .

The sign test is performed to test $H _ { 0 } : m = 45 \text { versus } H _ { 1 } : m \neq 45 \text {. }$ There are 15 positive signs and 7 negative signs. What is the value of the test statistic?

The following table lists values measured for 10 consecutive eruptions of the geyser Old Faithful in Yellowstone National Park. They are the duration, in minutes, of the eruption $\left( x _ { 1 } \right)$ the dormant period before the eruption $\left( x _ { 2 } \right)$ and the dormant period after the eruption ( y ). y 4.1 70 79 3.7 79 60 3.8 60 86 3.4 86 71 4.0 71 67 2.3 67 81 4.4 81 76 4.1 76 83 4.3 83 76 3.3 76 55 Construct the multiple regression equation $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$

Given $n _ { 1 } = 15 , n _ { 2 } = 21 , \mathrm {~S} = 258.5 , \text { and } H _ { 1 } : m _ { 1 } \neq m _ { 2 } ,$ compute $\sigma _ { s }$

The number of visits to a certain web site were counted each day of a particular week. ) Day Number of Visits Sunday 147 Monday 76 Tuesday 146 Wednesday 134 Thursday 132 Friday 160 Saturday 132 Test the hypothesis that web site visits are equally likely to occur on any day of the week. $\alpha = 0.01$ level of significance.

In a study of reaction times,) Visual Auditory 201 241 164 237 189 243 168 243 190 244 239 247 169 237 236 244 Construct a $99 \%$ confidence interval for the mean auditory response time for subjects witl a visual response time of 171 .

Find the critical value at the $\alpha = 0.05$ level for the following sample, for testing $H _ { 0 }$ m= 48 versus $H _ { 1 } : m > 48$ . 30 52 55 48 41 64 57 41 48 52 51 39 66 61

The following table presents the numbers of cucumber seeds,) Brand A Brand B Brand C Brand D Germinated 44 33 35 31 Failed to Germinate 10 9 2 17 Can you conclude that the the germination rate is related to the brand of seed? Use the $\alpha = 0.01$ level of significance.

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 binder content be interpreted? If so, interpret the main effect. I $\alpha = 0.01$ level of significance.

A psychology instructor gave a five-question true-false quiz to her class of 178 students. ) Number Correct 0 1 2 3 4 5 Observed 8 30 56 48 26 10 The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5. Under the null hypothesis, the number Of correct answers has a binomial distribution with 5 trials and success probability 0.5. Perform a chi-square test of this hypothesis. Can you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?

level Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 5 , n _ { 2 } = 7$ , and $n _ { 3 } = 8$ . The sample means were $\bar { x } _ { 1 } = 2.66 , \bar { x } _ { 2 } = 2.10$ , and $\bar { x } _ { 3 } = 1.79$ . The sample standard deviations were $s _ { 1 } = 0.48 , s _ { 2 } = 0.33$ , and $s _ { 3 } = 0.32$ . The grand mean is $\bar { x } = 2.116$ Can you conclude that two or more of the population means are different? Use the $\alpha = 0.1$ of significance.