1. A veterinary researcher takes an SRS of 60 horses presenting with colic. The
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Question
1. A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60 horses with colic is 12 years. The average age of horses seen at the veterinary clinic was determined to be 10 years. The researcher concludes that horses with colic are older. The value 12 is a:
sample mean.
population mean.
None of the above
variance of the sample mean.
2.
The Department of Motor Vehicles reports that 32% of all vehicles registered in the state are made by a Japanese or European automaker. The number 32% is best described as
a sample proportion.
a statistic.
a parameter.
3.
At a certain driver's license testing station only 40% of all new drivers pass the behind-the-wheel test the first time they take it. A sample of 50 new drivers from a certain high school found that 36% of them had passed the test the first time. Which of these numbers is a statistic?
36%
50
40%
4.
The sampling distribution of a statistic is the:
mechanism that determines whether randomization was effective.
extent to which the sample results differ systematically from the truth.
probability that we obtain the statistic in repeated random samples.
distribution of values taken by a statistic in all possible samples of the same size from the same population.
5.
The law of large numbers states that as the number of observations drawn at random from a population with finite mean increases, the mean of the observed values:
fluctuates steadily between one standard deviation above and one standard deviation below the mean.
gets larger and larger.
gets smaller and smaller.
tends to get closer and closer to the population mean .
6.
(15.22) 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 in the population of all ELBW babies. This means that :
in many samples from this population, the mean of the many values of x will be equal to .
in many samples from this population, the many values of x will have a distribution that is close to Normal.
as we take larger and larger samples from this population, x will get closer and closer to .
7.
(15.23) The number of hours a battery lasts before failing varies from battery to battery. The distribution of failure times follows an exponential distribution (see Example 15.8), which is strongly skewed to the right.
The distribution of burnout times is strongly skewed to the right. The central limit theorem says that :
the average failure time of a large number of batteries has a distribution that is close to Normal.
the average failure time of a large number of batteries has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs.
as we look at more and more batteries, their average failure time gets ever closer to the mean for all bulbs of this type.
8.
An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was = 119.6 ounces. Suppose the standard deviation is known to be = 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean . If the sample size of birth records increases, how does the sampling distribution change?
The shape of the distribution will change, but it is not possible to determine what the new distribution will be without knowing the new data.
The shape of the distribution will change, but it is dependent upon the new data that is collected.
The sampling distribution will remain Normal and the mean will remain the same regardless of the sample size, but its standard deviation will be smaller than the sampling distribution based on the smaller sample.
The sampling distribution will remain Normal regardless of the sample size, and will have the same average and standard deviation as the sampling distribution computed from the smaller sample.
9.
A random sample of n = 25 flights was taken and the time recorded to board the flight. It was found that minutes. Previous studies had determined boarding times to be normally distributed with = 38 minutes and = 36 minutes. The sampling distribution of , the sample average in samples of size n = 25 is:
N(38, 36).
N(38, 1.2).
N(42, 36).
N(38, 7.2).
10.
A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60 horses with colic is 12 years. The average age of horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of horses coming to the veterinary clinic is 8 years. The probability that a sample mean is 12 or larger for a sample from the horse population is:
0.9736.
0.1264.
0.0264.
0.0100.
11.
The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed. The probability that the average age, of the 100 residents selected is less than 68.5 years is:
0.805.
0.043.
0.568.
0.195.
12.
Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. If each firm randomly selects 3% of its employees, which statement is TRUE about the sampling distributions of the sample means?
The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company (Company B) because a larger sample is being selected.
The sampling distributions of the sample means will have about the same standard deviation because in both cases we're selecting 3% of the employees.
The smaller company (Company A) will have a sampling distribution with smaller standard deviation.
None of the above
13.
The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. The distribution of the sample mean of the weights of cheese wedges is:
approximately Normal, mean 8.1, standard deviation 0.2.
approximately Normal, mean 8.1, standard deviation 0.020.
approximately Normal, mean 8.1, standard deviation 0.063.
It is not possible to tell because the sample size is too small.
14.
In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 115 is:
0.528.
0.981.
0.452.
0.019.
15.
As the sample size n increases, what does the mean of the distribution of the sample mean do?
increases
decreases
remains constant
16.
As the sample size n increases, what does the standard deviation of the distribution of the sample mean do?
increases
decreases
remains constant
1. A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60 horses with colic is 12 years. The average age of horses seen at the veterinary clinic was determined to be 10 years. The researcher concludes that horses with colic are older. The value 12 is a:
sample mean.
population mean.
None of the above
variance of the sample mean.
Explanation / Answer
Solution:-
1) option A. sample mean
2) option C. a parameter.
3) option A. 36%
4) option D. distribution of values taken by a statistic in all possible samples of the same size from the same population.
5) option D. tends to get closer and closer to the population mean .
6) option A. in many samples from this population, the mean of the many values of x will be equal to .
7) option C. as we look at more and more batteries, their average failure time gets ever closer to the mean for all bulbs of this type.
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