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Chapter 7: Q. 56 (page 479)
Making auto parts Refer to Exercise 54 . How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of to be ? Justify your answer.
If the sample's standard deviation of the sampling distribution is , the sample should be 16 axles.
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Cold cabin? The dotplot shows the results of taking SRSs of temperature readings from a Normal population with and and recording the sample standard deviation each time. Suppose that the standard deviation from an actual sample is . What would you conclude about the thermostat manufacturer's claim? Explain your reasoning.
The number of undergraduates at Johns Hopkins University is approximately 2000 , while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80 at both schools. Which of the following is the best conclusion?
a. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it comes from a smaller population.
b. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it is based on a smaller sample size.
c. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it comes from a larger population.
d. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it is based on a larger sample size.
e. We expect that the estimate from Johns Hopkins will be about the same distance from the truth as the estimate from Ohio State because both samples are 3 % of their populations.
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. reduce the bias and variability of the estimate.
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard deviation ounce. Assume that the machine is working properly. If 4 bottles are randomly selected and the number of ounces in each bottle is measured, then there is about a probability that the sample mean will fall in which of the following intervals?
a. to ounces
b. to ounces
c. to role="math" localid="1654391534650" ounces
d. to ounces
e. to ounces
The probability distribution for the number of heads in four tosses of a coin is given by
| Number of heads | 0 | 1 | 2 | 3 | 4 |
| Probability | 0.0625 | 0.2500 | 0.3750 | 0.2500 | 0.0625 |
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
e. 0.0625
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