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Chapter 7: Q. 23 (page 456)

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13to 16year-olds. The researchers will report the mean xfrom their sample as an estimate of the mean cholesterol level 渭in this population. Explain to someone who knows little about statistics what it means to say that xis an unbiased estimator of 渭.

Short Answer

Expert verified

xis an unbiased estimator of 渭if total of all conceivable mean values equals 渭

Step by step solution

01

Given Information

We need to explain how xis an unbiased estimator of渭.

02

Explanation

xis an unbiased estimator of 渭if total of all conceivablexis equal to渭. xisn't systematically higher or lower than; in other words, it doesn't have a strong propensity to underestimate or overestimate.

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Most popular questions from this chapter

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x-x炉=810grams. This sample mean is an unbiased estimator of the mean weight 渭 in the population of all ELBW babies, which means that

a. in all possible samples of size 219 from this population, the mean of the values of x-x炉will equal 810 .

b. in all possible samples of size 219 from this population, the mean of the values of x-x炉will equal 渭

c. as we take larger and larger samples from this population, x-x炉will get closer and closer to 渭.

d. in all possible samples of size 219 from this population, the values of x-x炉will have a distribution that is close to Normal.

e. the person measuring the children's weights does so without any error.

In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is

a. left-skewed with mean 122 and standard deviation 0.35.

b. exactly Normal with mean 122 and standard deviation 5.

c. exactly Normal with mean 122 and standard deviation 0.35.

d. approximately Normal with mean 122 and standard deviation 5.

e. approximately Normal with mean 122 and standard deviation 0.35.

The candy machine Suppose a large candy machine has 45%orange candies, Use Figures 7.11and7.12(page 434) to help answer the following questions.

(a) Would you be surprised if a sample of 25candies from the machine contained 8orange candies (that's 32%orange)? How about 5orange candies ( 20%orange)? Explain.

(b) Which is more surprising getting a sample of 25candies in which 32%are orange or getting a sample of 50candies in which 32%are orange? Explain.

Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent 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 POV鈭�=59.2-0.620(HSGR) POV^=59.2-0.620(HSGR) with r2=0.802r2=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 percent of families living in poverty is predicted to decrease by approximately 0.896 .

b. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.802.

c. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.620.

d. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.802.

e. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.620.

Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam?

a. It means that you missed two questions on the exam.

b. It means that you got twice as many questions correct as the average student.

c. It means that your grade was 2 points higher than the mean grade on this exam.

d. It means that your grade was in the upper 2% of all grades on this exam.

e. It means that your grade is 2 standard deviations above the mean for this exam.
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