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Chapter 7: Q.46 (page 441)
The sampling distribution of is approximately Normal because
(a) there are at least Division I college athletes.
(b) and .
(c) a random sample was chosen.
(d) a large sample size like guarantees it.
(e) the sampling distribution of always has this shape.
The correct answer is (b)and.
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The Gallup Poll has decided to increase the size of its random sample of voters from about people to about 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
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 inches and standard deviation inches. To see if this distribution applies at their high school, an AP Statistics class takes an SRS of of the -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 ? To find out, we used Fathom software to simulate choosing SRSs of size students from a population that is . 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 ? Justify your answer.
(b) Describe the distribution. Are there any obvious outliers?
(c) Suppose that the average height of the girls in the class鈥檚 actual sample is . What would you conclude about the population mean height for the -year-old females at the school? Explain.
A machine is designed to fill -ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is ounces with a standard deviation of ounces. Assume that the machine is working properly. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then of the observations should occur in which interval?
(a) to ounces
(b) to ounces
(c) to ounces
(d) to ounces
(e) None of the above
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 states and the District of Columbia, and a regression analysis was conducted. The resulting least-squares regression line is given by (HSGR) with . Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?
(a) For each increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately .
(b) For each increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately .
(c) For each increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately .
(d) For eachincrease in the percentage of families living in poverty, the graduation rate is predicted to increase by approximately .
(e) For each increase in the per cent of families living in poverty, the graduation rate is predicted to decrease by approximately.
Which of the following statements about the sampling distribution of the sample mean is incorrect? (a) The standard deviation of the sampling distribution will decrease as the sample size increases.
(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.
(c) The sample mean is an unbiased estimator of the true population mean.
(d) The sampling distribution shows how the sample mean will vary in repeated samples.
(e) The sampling distribution shows how the sample was distributed around the sample mean
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