The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assign ing line positions on voting ballots. Among 4 l different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line. Find the probability of exactly 40 top lines for Democrats.

The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assign ing line positions on voting ballots. Among 4 l different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 40 top lines for Democrats significantly high?

A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) follow.

$$\begin{matrix} \text{ } & \text{ } & \text{Gasoline} & \text{Brands} & \text{ }\\ \text{ } & \text{ } & \text{I} & \text{II} & \text{III}\\ \text{ } & \text{A} & \text{18} & \text{21} & \text{20}\\ \text{ } & \text{B} & \text{24} & \text{26} & \text{27}\\ \text{Automobiles} & \text{C} & \text{30} & \text{29} & \text{34}\\ \text{ } & \text{D} & \text{22} & \text{25} & \text{24}\\ \text{ } & \text{E} & \text{20} & \text{23} & \text{24}\\ \end{matrix}$$

                a. At $\alpha =$ .05, is there a significant difference in the mean miles-per-gallon characteristics

of the three brands of gasoline? b. Analyze the experimental data using the ANOVA procedure for completely randomized designs. Compare your findings with those obtained in part (a). What is the advantage of attempting to remove the block effect?

Fuel Efficiency of Gasoline Brands. A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) follow. Gasoline Brands

$$\begin{array}{lcccc} & & \text { I } & \text { II } & \text { III } \\ & \text { A } & 18 & 21 & 20 \\ \text { Automobiles } & \text { B } & 24 & 26 & 27 \\ & \text { C } & 30 & 29 & 34 \\ & \text { D } & 22 & 25 & 24 \\ & \text { E } & 20 & 23 & 24\end{array}$$

b. Analyze the experimental data using the ANOVA procedure for completely randomized designs. Compare your findings with those obtained in part (a). What is the advantage of attempting to remove the block effect?

Assume that different groups of couples use the XS ORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 16 couples. Is the result of 11 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method?

Fuel Efficiency of Gasoline Brands. A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) follow.

$$\begin{aligned} &\text { Gasoline Brands }\\ &\begin{array}{ccccc} & & \text { I } & \text { II } & \text { III } \\ & \text { A } & 18 & 21 & 20 \\ \text { Automobiles } & \text { B } & 24 & 26 & 27 \\ & \text { C } & 30 & 29 & 34 \\ & \text { D } & 22 & 25 & 24 \\ & \text { E } & 20 & 23 & 24 \end{array} \end{aligned}$$

At = 5 .05, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline?

Automobile Selection An automobile dealer has $12$ small automobiles, $8$ mid-size automobiles, and $6$ large automobiles on his lot. How many ways can two of each type of automobile be selected from his inventory?

Determine |V| for the following graphs or multigraphs G. a) G has nine edges and all vertices have degree 3. b) G is regular with 15 edges. c) G has 10 edges with two vertices of degree 4 and all others of degree 3.

A county clerk in Essex County, New Jersey, selected candidates for positions on election ballots. Democrats were selected first in 40 of 41 ballots. Because he was supposed to use a method of random selection, Republicans claimed that instead of using randomness, he used a method that favored Democrats. Use a 0.01 significance level to test the claim that the ballot selection method favors Democrats.

How is the economic and social well-being of the United States determined?

Make a table and graph for $h ( x ) = x ^ { 3 } – 4$ Find the domain, range, and intercepts.

A bank wants to estimate the proportion of its checking account customers who prefer to deposit checks in their account using a smartphone rather than making deposits at the local branch bank. Describe how the bank could select an SRS of 100 account holders.

Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. $$ $Males have pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute. Is a pulse rate of 50 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.) Explain. $$

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0. 75 probability that a pea has green pods (as in one of Mendel's famous experiments). Assume that offspring peas are randomly selected in groups of 16. Is a result of 7 peas with green pod a result that is significantly low? Why or why not?