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. What do the results suggest about how the clerk met the requirement of assigning the line positions using a random method?

Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.

The County Clerk in Essex County, New Jersey, was responsible for randomly assigning the order in which candidates’ names appeared on a recent election ballot. Among 41 different ballots, a Democrat was placed on the first line 40 times, and a Republican was placed on the first line once.

The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.

Which probability is relevant for determining whether 40 first lines for Democrats is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 first lines for Democrats significantly high?

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.

Castaneda v. Partida is an important court case in which statistical methods were used as part of a legal argument. When reviewing this case, the Supreme Court used the phrase "two or three standard deviations" as a criterion for statistical significance. This Supreme Court review has served as the basis for many subsequent applications of statistical methods in legal settings. (The two or three standard deviations referred to by the Court are values of the $z$ statistic and correspond to P-values of approximately 0.05 and 0.0026.) In Castaneda, the plaintiffs alleged that the method for selecting juries in a county in Texas was biased against Mexican Americans. For the period of time at issue, there were 181,535 persons eligible for jury duty, of whom 143,611 were Mexican Americans. Of the 870 people selected for jury duty, 339 were Mexican Americans. What proportion of eligible voters were Mexican Americans? Let this value be $p_0$.

In "The Overtime Rule in the National Football League: Fair or Unfair?" by Gorgievski et al., MathAMATYC Educator, Vol. 2, No. I, the authors report that among 414 football games won in overtime, 235 were won by the team that won the coin toss at the beginning of overtime. Using a $0.05$ significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it.

Use the given probability value to determine whether the sample results are significant.

The County Clerk in Essex, New Jersey, was supposed to use randomness to assign the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democratic candidate names were placed on the first line 40 times. The probability of a result that high is 0.0000000000191. Assuming randomness was used, is the result of 40 Democratic candidate names being placed on the first line significantly low, significantly high, or neither?

Eliminate the parameter and sketch the graphs. $x = 2 t ^ { 2 }$, $y = t ^ { 4 } + 1$

Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.

In a study of the Ornish weight loss program, 40 subjects lost a mean of 3.3 lb after 12 months (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction,” by Dansinger et al., Journal of the American Medical Association, Vol. 293, No. 1). Methods of statistics can be used to show that if this diet had no effect, the likelihood of getting these results is roughly 3 chances in 1000.

Use the given sample space or construct the required sample space to find the indicated probability. Use this sample space listing the eight simple events that are possible when a couple has three children:

{bbb, bbg, bgb, bgg, gbb,gbg, ggb, ggg} .

Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is ex actly one girl.

Find the probability and answer the questions. MicroSort's YSORT gender selection technique is designed to increase the likelihood that a baby will be a boy. At one point before clinical trials of the YSORT gender selection technique were discontinued, 291 births consisted of 239 baby boys and 52 baby girls (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a boy born to a couple using MicroSort's YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy?

Vitamin $B_{12},$ cyanocobalamin, is essential for human nutrition. It is concentrated in animal tissue but not in higher plants. Although nutritional requirements for the vitamin are quite low, people who abstain completely from animal products may develop a deficiency anemia. Cyanocobalamin is the form used in vitamin supplements. It contains 4.34% cobalt by mass. Calculate the molar mass of cyanocobalamin, assuming that there is one atom of cobalt in every molecule of cyanocobalamin.

Identify the graph of the given equation.

$$3 x ^ { 2 } = y ^ { 2 } - 1$$

AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic. When purchasing bulk orders of AAA batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 2000 AAA batteries, and 2% of them do not meet specification . What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?