Statistics Quiz/Test 2
For some value of z, the probability that a standard normal variable is below z is 0.2090. The value of z is:
-0.81
Which of the following is NOT a reason for the need for sampling?
it is sometimes destructive to observe the entire population
When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be, the _______ the sample size required.
larger
When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be, the __________ the sample size required
larger
The standard error of the mean
measures the variability of the mean from sample to sample
In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ________ interval
narrower
The width of a confidence level estimate for a proportion will be
narrower for 90% confidence than for a 95% confidence
For sample size 1, the sampling distribution of the mean will be normally distributed
only if the population is normally distributed
the t test for the mean difference between 2 related populations assumes that the
population of differences is approximately normal or sample sizes are large enough
The t test for the difference between the means of 2 independent population assumes that the respective
populations are approximately norma
According to the Central Limit Theorem,
sample size is important when the population is not normally distributed
What is the difference between a sample mean and the population mean called?
sampling error
Sampling distributions describe the distribution of
statistics
When constructing a confidence interval for a population mean, if a population is normally distributed and a small is taken, then the distribution of is based on ______ distribution
t
The "t" distribution approaches the ________ as the sample size ________
Z, increases
True or False: The sample proportion is an unbiased estimate of the population proportion
True
Which of the following statements is not true?
the probability of making a type 2 error and level of significance are the same
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors were selected. Suppose that the test statistics is -2.20. Can we conclude that H0 should be rejected at the a) =.10, b) =0.05, and c) =0.01 level of type 1 error?
yes, yes, no
True or False: if the population is symmetric, the sampling distribution of the mean can be approximated by the normal distribution samples that contain at least 15 observations.
True
For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed
regardless of the shape of the population
True or False: As the sample size increases, the standard error of the mean increases.
False
For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3340. The value of Z is
0.97
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50.50 and s^2 = 400 . Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal
$50.50 +- $11.08
The t distribution
all of the above
Referring to Table 7-2, without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie?
$114,000 -- $116,000
A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients die would receive payments beyond age 75?
0.0228
The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71.
0.0228
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. Referring to Table 7-7, the standard error of all possible sample proportions is ______.
0.0342
Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z is between -2.89 and -1.03 is
0.1496
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 52 minutes?
0.4974
The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to:
2.80
A confidence interval increases in width as: A. the level of confidence increases B. n decreases C. s increases D. All of the above
All of the above
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" as an inference
In repeated sampling, 95% of the intervals constructed would contain the population mean.
Sales prices of baseball cards from the 1960s are known to possess a skewed-rich distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.
Normal with a mean of $5.35 and a standard error of $0.28
Which of the following would be an appropriate null hypothesis? ______
The mean of a population is equal to 60
Which of the following statements about the sampling distribution of the sample mean is incorrect ?
The standard deviation of the sampling distribution of the sample mean is equal to o (sigma)
The Central Limit Theorem is important in statistics because
for a large n, it says the sampling distribution of the sample mean is approximately normal regardless of the shape of the population
Which of the following statements about the sampling distribution of the sample mean is incorrect?
the standard deviation of the sampling distribution of the sample mean is equal to 0 (fancy zero)
The "t" distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown
true
In its standardized form, the normal distribution:
has a mean of 0 and a standard deviation of 1
For some positive value of Z, the probability that a standard normal variable is below Z is 0.2090. The value of Z is
-0.81
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken. Referring to Table 7-2, without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie
$114,000-$116,000
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: and s^2. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.
$50.50 +- $11.08
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:
-2.33
A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The p-value associated with the test statistic in this problem is approximately equal to
.0026
According to an article, 19% of the entire US population have high-speed access to the Internet. Random samples of size 200 are selected from the US population. Among all the random samples of size 200, _________% will have more than 30% who have high-speed across to the internet.
0
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. What is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the website?
0.0015
Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z is less than -2.20 is
0.0139
A company that sells annuities must base the annual payout on the probability distribution of the length of life the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?
0.0228
The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be over 125 inches in length?
0.0228
According to an article, 19% of the entire US population have high-speed access to the Internet. Random samples of size 200 are selected from the US population. The standard error of all the sample proportions is _______
0.0277
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 centimeters?
0.042
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. The standard deviation of all the sample proportions of customers who will make a purchase after visiting the website is
0.05050
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88 minutes is __________.
0.0548
A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, the standard error of the proportions of students in the samples who are minority students is ________.
0.05745
A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounces. Find the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces
0.0668
The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is
0.0668
The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is
0.1056
For some positive value of x, the probability that a standard normal variable is between 0 and +2x is 0.1255. The value of x is:
0.16
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 35.98 is ________.
0.1891
A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, the probability that more than half of the students on the sample will be minority students
0.1920
A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients die before they reach the standard retirement age of 65?
0.1957
Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z is more than 0.77 is
0.2207
A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more that 4.5 minutes will hang up before placing an order?
0.22313
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. What is the probability that the sample mean is more than 3 hours below the population mean?
0.2266
If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes is
0.3085
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. What is the probability that the sample mean of the population mean by more than 2 hours?
0.3085
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken Referring to Table 7-2, what is the probability that the sample mean selling price was between $114,000 and $116,000?
0.3108
The value of the cumulative standardized normal distribution at z is 0.6255. The value of z is:
0.32
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is _____________.
0.3446
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. What is the probability that the sample mean differs from the population mean by less than 2 hours?
0.3830
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. What is the probability that the sample mean differs from the population mean by more than 3 hours?
0.4532
The probability that a standard normal variable Z is positive is
0.50
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken. What is the probability that the sample mean selling price was between $113,000 and $117,000?
0.5762
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken Referring to Table 7-2, what is the probability that the sample mean selling price was between $113,000 and $117,000?
0.5763
The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is
0.5865
A catalog company that receives the majority of orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?
0.60653
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is ________.
0.6554
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be between 77 and 89 minutes is ______
0.6898
Which of the following is NOT true about the student's "t" distribution?
It is used to construct confidence intervals for the population mean when the population standard deviation is known
If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.
0.7745
Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that is between -0.88 and 2.29 is
0.7996
A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, the probability is _____ that between 30% and 50% of the students in the sample will be minority students
0.8034
The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be between 121 and 124 inches?
0.8186
Suppose Z has a standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z is more than -0.98 is
0.8365
The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. Referring to Table 7-3, what is the probability that the sample mean lifetime is more than 1,550 hours?
0.8413
The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be less than 124 inches?
0.8413
Suppose Z has the standardized normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z is less than 1.15 is
0.8749
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?
0.8767
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is less than 36.03 oz. is _____________.
0.8849
A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounces. Find the proportion of all jars packaged by this process that have weights that fall above 10.875 ounces
0.8944
Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.
0.9104
Given that x is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that x is between 47 and 54.
0.9104
0.8340. The value of z is
0.97
For some positive value of z, the probability that a standard normal variable is between 0 and z is 0.3340. The value of z is:
0.97
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken. What is the probability that the sample mean selling price was more than $110,000?
0.9772
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken. Referring to Table 7-2, what is the probability that the sample mean selling price was more than $110,000?
0.9772
Suppose Z has a standard normal distribution with a mean of 0 and a standard deviation of 1. The probability that Z is between -2.33 and 2.33 is
0.9802
For sample size 16, the sampling distribution of the mean will be approximately normally distributed
if the shape of the population is symmetrical
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz is __________.
0.9836
The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. Referring to Table 7-3, the probability is 0.15 that the sample mean lifetime is more than how many hours?
1,651.82 hours
The power of a test is denoted by
1-
For some positive value of x, the probability that a standard normal variable is between 0 and +1.5x is 0.4332. The value of x is:
1.00
The value of the cumulative standardized normal distribution at 1.5x is 0.9332. The value of x is:
1.00
For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is
1.16
For some positive value of z, the probability that a standard normal variable is between 0 and z is 0.3770. The value of z is:
1.16
Referring to table 8-3, the confidence goes from _________ to _______
12.09 to 12.19
You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 86% of the time lapsed will fall between which two numbers?
13 seconds and 17 seconds
You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 14 and 15 seconds?
14 seconds
You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 60% of the time lapsed will fall between which two numbers?
14 seconds and 16 seconds
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. The average of all the sample proportions of customers who will make a purchase after visiting the website is
15%
According to an article, 19% of the entire US population have high-speed access to the Internet. Random samples of size 200 are selected from the US population. The population mean of all the sample proportions is ________.
19%
The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds) do 89.80% of the weights occur?
2.184 pounds
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score greater than 95?
2.27%
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What would you expect the standard error of the mean to be?
2.5 minutes
A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine Referring to Table 8-3, the critical value to use in obtaining the confidence interval is
2.58
If you were a 99% confidence interval of the population mean based on a sample of n=25, where the standard deviation of the sample s=0.05, the critical value of "t" will be
2.7970
If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the distribution that 75.8% of the college students exceed when trying to find a parking spot in the library parking lot
2.8 minutes
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. Referring to Table 7-7, 95% of the samples proportions symmetrically around the population proportion will have between _____% and_____% of the customers who take advantage of online customer service.
30.79 and 44.21
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. Referring to Table 7-7, 90% of the samples proportions symmetrically around the population proportion will have between _____% and_____% of the customers who take advantage of online customer service.
31.87 and 43.13
A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 95% of the samples will have more than ______% of minority students
35.55
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. Referring to Table 7-7, the population mean of all possible sample proportions is ______.
37.5%
If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
38
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 90 and 95?
4.41%
The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established?
4.84 pounds
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. So, 95% of all sample means will fall between what two values?
40.1 and 49.9 minutes
The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. So, 90% of the sample means will be greater than what value?
41.8 minutes
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and 75?
43.32%
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 75 and 90?
43.32%
A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ______% of minority students
49.83
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling distribution of the sample mean is ______ minutes.
5
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. Referring to Table 7-7, ____ % of the samples are likely to have less than 37.5% who take advantage of online customer service.
50
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. Referring to Table 7-7, ____ % of the samples are likely to have between 35% and 40% who take advantage of online customer service.
53.48
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 95.46% of the students will score between which two scores?
55 and 95
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 96.54% of the students will score between which two scores?
60 and 90
The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. Referring to Table 8-2, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.
63
According to an article, 19% of the entire US population have high-speed access to the Internet. Random samples of size 200 are selected from the US population. Among all the random samples of size 200, ______ % will have less than 20% who have high-speed access to the internet.
64.08
The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. Referring to Table 7-3, the probability that the sample mean lifetime differs from the population mean lifetime by at least how many hours?
64.08 hours
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?
67%
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. So, 95% of the sample means based on samples of size 64 will be between ________ and ________.
70.2 and 89.8
According to an article, 19% of the entire US population have high-speed access to the Internet. Random samples of size 200 are selected from the US population. Among the random sample of size of 200, ________% will have between 9% and 29% who have high-speed access to the Internet
99.97
A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants
71.78 years old
A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.
71.78 years old
Referring to Table 8-2, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence. Referring to Table 8-2, due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88.0 points. A 90% confidence interval would go from ________ to ________.
82.12 or 93.88
You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and 95?
91.05%
According to an article, 19% of the entire US population have high-speed access to the Internet. Random samples of size 200 are selected from the US population. Among all the random samples of size 200, __________% will have between 14% and 24% who have high-speed access to the internet.
92.85
You know that the probability of committing a Type II error (α) is 5%, you can tell that the power of the test is
95%
A major department store chain is interested in estimating the average amount of its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50,50 and s^2 = 400. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ ?
A t distribution with 14 degrees of freedom
In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?
A test for the difference between the means of 2 related populations
The distribution of the number of loaves of bread sold per day by a large bakery over the past 5 years has a mean of 7.750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 days has been selected. What is the approximate probability that the average number of loaves sold in the sampled days exceeds 7,895 loaves?
Approximately 0
How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the test statistics does fall in the rejection region at =0.05. Which of the following decisions is correct?
At = 0.05 we reject H0
Which of the following about the normal distribution is NOT true?
It is a discrete probability distribution
Which of the following about the normal distribution is NOT true?
It is a discrete probability of distribution
For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.
Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 26 bottles filled by this machine. The sampling distribution of the sample mean has a standard error of 0.15.
False
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The sampling of the sample mean will be approximately normal only if the population sample is normal.
False
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?
Increase the sample size and decrease the confidence level
Based on the Central Limit Theorem the size of the sampling error is
Inversely related to the sample size, i.e., the larger the sample size the smaller the sampling error
Which of the following is true regarding the sampling distribution of the mean for a large sample size?
It has a normal distribution with the same mean as the population but with a smaller standard deviation
How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the alternative we wanted to test was H1: < 60 State the correct rejection region for =0.05
Reject H0 if t <- 1.6604
The power of a test is measured by its capability of ______
Rejecting a null hypothesis that is false
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors were selected. Suppose you reject the null hypothesis. What conclusion can you draw?
There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.
True or False: The sample mean is an unbiased estimate of the population mean
True
True or False: The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.
True
True or False: if the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations
True
True or False: the amount of time it takes to complete and examination has a skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students, were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.
True
In a particular batch of data that is approximately normally distributed, we would find that
all the above
If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000
a one-tailed test should be utilized
If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000
a two-tailed test should be utilized
The standard error of the mean: 1. is never larger than the standard deviation of the population. 2. decreases as the sample size increases 3. measures the variability of the mean from sample to sample. 4. all the above
all the above
The t distribution
all the above
When determining the sample size, if the value found is not an integer initially the next highest integer value will ___________ be chosen
always
As the size of the sample increases, what happens to the shape of the distribution of sample means?
approaches a normal distribution
Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million
approximately 1
The standard error of the proportion will become larger
as p approaches 0.50
A sample that does not provide a good representation of the population from which it was collected is referred to as a(n) _______ sample
biased
A 99% confidence interval estimate can be interpreted to mean that
both of the above
The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would
increase the sample size to 400
When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that π is estimated to be, the sample size required ________.
is larger
For a given sample size n, if the level of significance decreased, the power of the test will:
decrease
All possible sample sizes of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means?
exactly the same as the population mean
The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. True or False: Referring to Table 8-2, this confidence interval is only valid if the scores on the Fortunato test are normally distributed
false
The Central Limit Theorem is important in statistics because
for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population
In its standardized form, the normal distribution
has a mean of 0 and a standard deviation of 1
How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Using the sample information provided, calculate the value of the test statistic
t= (52-60)/(22/100^2)
Which of the following would be an appropriate alternative hypothesis?
the mean of a population is greater than 70
which of the following is true about the sampling distribution of the sample mean?
the mean of the sampling distribution is always
If the p-value is less than a in a two-tailed test
the null hypothesis should be rejected
The central limit theorem tells us that the sampling distribution is approximately normal. Which of the following conditions are necessary for the theorem to be valid?
the sample size has to be large
Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?
the standard deviation of the sample mean is equal to 3 years
A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The rental chain's conclusion from the hypothesis test using a 3% level of significance is:
to open a new store
A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The decision on the hypothesis test using a 3% level of significance is:
to reject Ho in favor of H1
