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AP2.23. There are four major blood types in humans: $\mathrm{O},\mathrm{A},\mathrm{B}$, and $\mathrm{AB}$. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-White, HawaiianChinese, and White. Suppose that a blood bank specimen is selected at random.

(a) Find the probability that the specimen contains type $\mathrm{O}$ blood or comes from the Hawaiian-Chinese ethnic group. Show your work.

(b) What is the probability that the specimen contains type AB blood, given that it comes from the Hawaiian ethnic group? Show your work.

(c) Are the events "type B blood" and "Hawaiian ethnic group鈥� independent? Give appropriate statistical evidence to support your answer.

Now suppose that two blood bank specimens are selected at random.

(d) Find the probability that at least one of the specimens contains type A blood from the White ethnic group.

Sale of eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer takes an SRS of $200$eggs from all the eggs shipped in one day. The laboratory reports that$9$of these eggs had salmonella contamination. Unknown to the producer, $0.1\%$(one-tenth of 1%) of all eggs shipped had salmonella. Identify the population, the parameter, the sample, and the statistic.

A study of voting chose $663$registered voters at random shortly after an election. Of these, $72\%$said they had voted in the election. Election records show that only$56\%$ of registered voters voted in the election. Which of the following statements is true about the boldface numbers?

(a)$72\%$is a sample; $56\%$is a population.

(b) $72\%$and$56\%$ are both statistics.

(c)$72\%$is a statistic and $56\%$is a parameter.

(d) $72\%$is a parameter and $56\%$is a statistic.

(e) $72\%$and$56\%$ are both parameters.

Identify the population, the parameter, the sample, and the statistic in each setting.

Stop smoking! A random sample of $1000$people who signed a card saying they intended to quit smoking were contacted nine months later. It turned out that $210$$(21\%)$of the sampled individuals had not smoked over the past six months.

Suppose that you are a student aide in the library and agree to be paid according to the 鈥渞andom pay鈥� system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is $\backslash (80$. If it comes up tails, your pay for the week is $\backslash )40$. You work for the library for $100$ weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x. The shape of the sampling distribution of xwill be

(a) Normal.

(b) approximately Normal

(c) right-skewed

(d) left-skewed.

(e) symmetric but not Normal.

Tall girls According to the National Center for Health Statistics, the distribution of heights for 16-year-old females is modeled well by a Normal density curve with mean $渭=64$inches and standard deviation $蟽=2.5$inches. To see if this distribution applies at their high school, an AP Statistics class takes an SRS of $20$of the $300$$16$-year-old females at the school and measures their heights. What values of the sample mean x would be consistent with the population distribution being $N(64,2.5)$? To find out, we used Fathom software to simulate choosing $250$SRSs of size $n=20$students from a population that is $N(64,2.5)$. The figure below is a dotplot of the sample mean height x of the students in the sample.

(a) Is this the sampling distribution of $x$? Justify your answer.

(b) Describe the distribution. Are there any obvious outliers?

(c) Suppose that the average height of the $20$girls in the class鈥檚 actual sample is $x=64.7$. What would you conclude about the population mean height $M$for the $16$-year-old females at the school? Explain.

Social scientists are interested in the association between the high school graduation rate (HSGR) and the percentage of U.S. families living in poverty (POV). Data were collected from all $50$states and the District of Columbia, and a regression analysis was conducted. The resulting least-squares regression line is given by $\overline{POV}=59.2-0.620$(HSGR) with $r^2=0.802$. Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?

(a) For each $1\%$increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately $0.896$.

(b) For each $1\%$increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately $0.802$.

(c) For each $1\%$increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately $0.620$.

(d) For each$1\%$increase in the percentage of families living in poverty, the graduation rate is predicted to increase by approximately $0.802$.

(e) For each $1\%$increase in the per cent of families living in poverty, the graduation rate is predicted to decrease by approximately$0.620$.

T7.11. Below are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked with an arrow on each histogram

Which statistic would provide the best estimate of the parameter? Justify your answer

Doing homework Refer to Exercise 9.

(a) Make a graph of the population distribution given that there are $3000$ students in the school. (Hint: What type of variable is being measured?)

(b) Sketch a possible graph of the distribution of sample data for the SRS of size $100$ taken by the AP Statistics students.

Tall girls Refer to Exercise 10.

(a) Make a graph of the population distribution.

(b) Sketch a possible graph of the distribution of sample data for the SRS of size $20$ taken by the AP Statistics class.