Question

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 = 810 grams. this sample mean is an unbiased estimator of the mean weight μ in the population of all elbw babies. this means that

Answer 1

The sample mean weight accurately estimates the population mean weight of extremely low birth weight babies without any bias.

Step-by-step explanation:

The statement that the sample mean weight of the 219 children in the study, with a mean weight of x = 810 grams, is an unbiased estimator of the mean weight μ in the population of all extremely low birth weight (ELBW) babies, means that the sample mean accurately estimates the population mean without any systematic error or bias. In other words, on average, the sample mean is equal to the population mean. This is important because it allows us to make inferences about the entire population based on the sample mean.

Answer 2

11.2 Florida voters. Florida played a key role in the 2000 and 2004 presidential elections. Voter registration records in August 2010 show that 41% of Florida voters are registered as Democrats and 36% as Republicans. (Most of the others did not choose a party.) To test a random digit dialing device that you plan to use to poll voters for the 2010 Senate elections, you use it to call 250 randomly chosen residential telephones in Florida. Of the registered voters contacted, 34% are registered Democrats. Is each of the boldface numbers a parameter or a statistic? Answer 41 % of registered voters are Democrats: parameter 36% of registered voters are Republicans: parameter 34% of voters contacted are Democrats: statistic 11.7 Generating a sampling distribution. Let’s illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the scores of 10 students on an exam: The parameter of interest is the mean score μ in this population. The sample is an SRS of size n = 4 drawn from the population. Because the students are labeled 0 to 9, a single random digit from Table B chooses one student for the sample. (a) Find the mean of the 10 scores in the population. This is the population mean μ. (b) Use the first digits in row 116 of Table B to draw an SRS of size 4 from this population. What are the four scores in your sample? What is their mean ? This statistic is an estimate of μ. (c) Repeat this process 9 more times, using the first digits in rows 117 to 125 of Table B. Make a histogram of the 10 values of . You are constructing the sampling distribution of . Is the center of your histogram close to μ? Answer (a) μ = 694/10 = 69.4. (b) The table below shows the results for line 116. Note that we need to choose 5 digits because the digit 4 appears twice. (c) The results for the other lines are in the table; the histogram is shown after the table.