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Chapter 7: Q 37. (page 462)
More SkittlesWhat sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b)? Justify your answer.
Sample size is
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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 grams. This sample mean is an unbiased estimator of the mean weight 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 will equal 810 .
b. in all possible samples of size 219 from this population, the mean of the values of will equal
c. as we take larger and larger samples from this population, will get closer and closer to .
d. in all possible samples of size 219 from this population, the values of will have a distribution that is close to Normal.
e. the person measuring the children's weights does so without any error.
Doing homework A school newspaper article claims that of the students at a large high school completed their assigned homework last week. Assume that this claim is true for the students at the school.
a. Make a bar graph of the population distribution.
b. Imagine one possible SRS of size from this population. Sketch a bar graph of the distribution of sample data.
refer to the following graph. Here is a dotplot of the adult literacy rates in 177 countries in a recent year, according to the United Nations. For example, the lowest literacy rate was 23.6 %, in the African country of Burkina Faso. Mali had the next lowest literacy rate at 24.0 %.
The overall shape of this distribution is
a. clearly skewed to the right.
b. clearly skewed to the left.
c. roughly symmetric.
d. uniform.
e. There is no clear shape.
According to government data, of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in
early childhood chooses an SRS of children from one state and finds that .
a. Find the probability that at least of the sample are from poverty-level householdshouseholds.
b. Based on your answer to part (a), is there convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of ? Explain your reasoning.
A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean . Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of will be half as big as when using a sample size of 160 . What sample size should the researcher use?
a. 40
b. 80
c. 320
d. 640
e. There is not enough information to determine the sample size.
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