91Ó°ÊÓ

Predict the election Just before a presidential election, a national opinion poll increases the size of its weekly random sample from the usual $1500$ people to $4000$ people.

(a) Does the larger random sample reduce the bias of the poll result? Explain.

(b) Does it reduce the variability of the result? Explain

Records from a random sample of dairy farms yielded the information below on the number of male and female calves born at various times of the day.

What is the probability that a randomly selected calf was
born in the night or was a female?
(a)$\frac{369}{513}$

(b)$\frac{485}{513}$

(c) $\frac{116}{513}$

(d)$\frac{116}{252}$

(e) $\frac{116}{233}$

Bias and variability The figure below shows his programs of four sampling distributions of different statistics intended to estimate the same parameter.

(a) Which statistics are unbiased estimators? Justify your answer. (b) Which statistic does the best job of estimating the parameter? Explain.

When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is$1.5$pounds with a standard deviation of $0.3$pounds, the mean weight of the packing material is $0.5$pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is$12$ pounds with a
standard deviation of$3$ pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?
(a)$1.84$
(b) $2.60$

(c) $3.02$

(d) $3.40$

(e)$9.10$

The Gallup Poll has decided to increase the size of its random sample of voters from about $1500$people to about $4000$people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

(a) reduce the bias of the estimate.

(b) increase the bias of the estimate.

(c) reduce the variability of the estimate.

(d) increase the variability of the estimate.

(e) have no effect since the population size is the same

identify the population, the parameter, the sample, and the statistic in each setting

Unemployment Each month, the Current Population Survey interviews a random sample of individuals in about $55,000$U.S. households. One of their goals is to estimate the national unemployment rate. In December $2009,10.0\%$of those interviewed were unemployed

(a) Sketch a possible graph of the distribution of sample data for an SRS of size $5$ with a range of $1000$grams.

(b) Explain why the dotplot of sample ranges above is not the actual sampling distribution of the sample range.

The probability distribution for the number of heads in four tosses of a coin is given by

The probability of getting at least one tail in four tosses of a coin is

(a) $0.2500$. (b)$0.3125$(c) $0.6875$(d)$0.9375$ (d) None of these

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of $13$- to $16$-year-olds. The researchers will report the mean $x$ from their sample as an estimate of the mean cholesterol level M in this population.

(a) Explain to someone who knows no statistics what it means to say that $x$is an unbiased estimator of $\mathrm{μ}$.

(b) The sample result x is an unbiased estimator of the population mean $\mathrm{μ}$ no matter what size SRS the study chooses. Explain to someone who knows no statistics why a large random sample gives more trustworthy results than a small random sample.

A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. A cumulative relative frequency graph is shown below from data collected over the past year. According to the graph, the shortest $80\%$of calls will take how long to complete?

(a) Less than$10$ minutes.
(b) At least$10$ minutes.
(c) Exactly$10$ minutes.
(d) At least$5.5$ minutes.
(e) Less than $5.5$minutes.