(1 pt) A poll conducted by a newspaper reported that 80% of those who responded
ID: 3331270 • Letter: #
Question
(1 pt) A poll conducted by a newspaper reported that 80% of those who responded liked ''reality TV.''
(a) The unknown true percentage of the population of all Americans who like ''reality TV'' is a
A. population.
B. parameter.
C. sample.
D. statistic.
(b) The number 80% is a
A. statistic.
B. sample.
C. parameter.
D. population.
The mean height of a certain population is 64.5 inches. Suppose we select ten people from this population at random and the mean of the heights of the ten people in the sample is 61.4 .
(a) The number 61.4 is a
A. statistic.
B. population.
C. parameter.
D. sample.
(b) The number 64.5 is a
A. statistic.
B. parameter.
C. sample.
D. population.
(a) A statistic is said to be unbiased if
A. it is used for only honest purposes.
B. the survey used to obtain the statistic was designed so as to avoid even the hint of racial or sexual prejudice.
C. both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful.
D. the mean of its sampling distribution is equal to the true value of the parameter being estimated.
(b) The sampling distribution of a statistic is
A. the probability that we obtain the statistic in repeated random samples.
B. the mechanism that determines whether or not randomization was effective.
C. the extent to which the sample results differ systematically from the truth.
D. the population consisting of all the possible values of the statistic that might be observed based on all possible samples of a given size.
(c) Sampling variation is caused by
A. changes in a population parameter from sample to sample.
B. random selection of a sample.
C. systematic errors in our procedure.
D. changes in a population parameter that cannot be predicted.
Suppose a random variable is normally distributed with =18 and =6.9. For samples of size 10:
(a) The mean of the sampling distribution of x¯ is
(b) The standard deviation of the sampling distribution of x¯ is
The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.8 grams per mile and standard deviation 0.17 grams per mile. Consider the sampling distribution of x¯ for samples of size n.
(a) If n = , the standard deviation of the sampling distribution of x¯ will be .01.
(b) If a smaller sample is considered, the standard deviation of the sampling distribution of x¯ will be . (NOTE: Enter ''SMALLER'',''LARGER'' or ''THE SAME'' without the quotes.)
For students in a certain region, scores of students on a standardized test approximately follow a normal distribution with mean =545.4 and standard deviation =29.1.
(a) What is the probability that a single randomly selected student from among all those in region who took the test will have a score of 549 or higher?
ANSWER:
For parts (b) through (e), consider a random sample of 35 students who took the test.
(b) The mean of the sampling distribution of x¯ is
(c) The standard deviation of the sampling distribution of x¯ is
(d) What z-score corresponds to the mean score of x¯ = 549?
ANSWER:
(e) What is the probability that the mean score x¯ of these 35 students will be 549 or higher?
ANSWER:
A company sells sunscreen in 300 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean =296 ml and standard deviation =5 ml. Suppose a store which sells this sunscreen advertises a sale for 4 tubes for the price of 3. Consider the average amount of lotion from a random sample of 4 tubes of sunscreen and find:
(a) The standard deviation of the sampling distribution of x¯ is
(b) The probability that the average amount of sunscreen in 4 randomly selected tubes will be less than 288 ml.
Answer:
An automobile insurer has found that repair claims are Normally distributed with a mean of $590 and a standard deviation of $550.
(a) Find the probability that a single claim, chosen at random, will be less than $550.
ANSWER:
(b) Now suppose that 100 claims are selected at random. Find the probability that the sample mean value of the 100 claims will be smaller than $550.
ANSWER:
(c) If a sample larger than 100 claims is considered, there would be chance of getting a sample with an average smaller then $550. (NOTE: Enter ''LESS'', ''MORE'' or ''AN EQUAL'' without the quotes.)
The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.2 ounces.
(a) What is the probability that the average weight of a random sample of 4 of these chocolate bars will be between 7.5 and 7.89 ounces?
ANSWER:
(b) For a random sample of of these chocolate bars, find the value L such that P(x¯<L)= 0.0281.
ANSWER:
Round answers below to three decimal places. Enter answers below as proportions (and not as percentages).
Of students at a large university, 22 percent are sophomores. For samples of 75 students, consider the sampling distribution of the sample proportion of sophomores.
(a) The mean of the sampling distribution of the sample proportion is .
(b) The standard deviation of the sampling distribution of the sample proportion is .
Round answers below to three decimal places. Enter answers below as proportions (and not as percentages).
Suppose that 60 percent of all consumers have a very favorable opinion of a certain product. A random sample of 96 consumers will be selected and the sample proportion who hold a very favorable opinion of the product will be determined.
(a) The probability that the sample proportion will be less than 0.6 .
(b) The probability that the sample proportion will be more than 0.68 is .
(c) The probability that the sample proportion will be between 0.46 and 0.63 .
Explanation / Answer
Ans:
1)
a)Parameter
b)Statistic
2)a)61.4 is statistic(sample mean)
b)64.5 is paramter(population mean
3) The sampling distribution of a statistic is
the population consisting of all the possible values of the statistic that might be observed based on all possible samples of a given size.
4)Suppose a random variable is normally distributed with =18 and =6.9. For samples of size 10:
(a) The mean of the sampling distribution of x¯ is =18
(b) The standard deviation of the sampling distribution of x¯ is =6.9/sqrt(10)=2.18
5)For students in a certain region, scores of students on a standardized test approximately follow a normal distribution with mean =545.4 and standard deviation =29.1.
z=(549-545.4)/29.1=0.124
P(z>0.124)=1-0.5493=0.4507
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