MATH-11-SP18: Module 3 Quiz
The symbol U-x represents the population mean of all possible sample means from samples of size n.
True
The symbol U^p represents the mean of all possible sample proportions from samples of size n.
True
When using the central limit theorem with n = 100, it is not necessary to assume the distribution of the population data is normally distributed.
True
If the data are quantitative and there are more than 30 numbers in the data set, then the distribution of this data will always be approximately normally distributed.
False
The number of seconds X after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to two decimal places. A. X ~ U( , ) Suppose that 50 classes are clocked then the sampling distribution is B. xBar~ N( , ) C. What is the probability that the average of 50 classes will end with the second hand between 25 and 35 seconds?
30 17.32 30 2.45 .96
For any sample of size 100, the population mean, the mean of the sampling distribution, and the sample mean will always be equal to each other.
False
The amount of coffee that people drink per day is normally distributed with a a mean of 16 ounces and a standard deviation of 5 ounces. 23 randomly selected people are surveyed. Round all answers to two decimal places. A. xBar~ N( , ) B. For the 23 people, find the probability that the average coffee consumption is between 15 and 18 ounces per day. C. What is the probability that one randomly selected person drinks between 15 and 18 ounces of coffee per day? D. Find the IQR for the average of 23 coffee drinkers. Q1 = Q3 = IQR:
16 1.04 .80 .34 15.3 16.70 1.4
The lengths of adult males' hands are normally distributed with mean 189 mm and standard deviation is 7.2 mm. Suppose that 30 individuals are randomly chosen. Round all answers to two decimal places. A. xBar~ N( , ) B. For the group of 30, find the probability that the average hand length is less than 190. C. Find the third quartile for the average adult male hand length for this sample size.
189 1.31 .78 189.88
The symbol -x represents the mean of the sample.
True
X ~ N(30,10). Suppose that you form random samples with sample size 4 from this distribution. Let xBar be the random variable of averages. Let ΣX be the random variable of sums. Round all answers to two decimal places. A. xBar~ N( , ) B. P(xBar<30) = 0.81 C. Find the 95th percentile for the xBar distribution. D. P(xBar > 36)= E. Q3 for the xBar distribution = 33.37
30 5 .5 38.22 .12 33.37
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. Round all answers to two decimal places. A. xBar~ N( , ) B. For the group of 16, find the probability that the average percent of fat calories consumed is more than 20. C. Find the third quartile for the average percent of fat calories.
36 2.5 1 37.69
Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.8 computers. 20 workers are randomly selected to work the next shift at the factory. Round all answers to two decimal places and assume a normal distribution. A. xBar~ N( , ) B. For the 20 workers, find the probability that their average number of computers put together per hour is between 3 and 5. C. If one randomly selected worker is observed, find the probability that this worker will put together between 3 and 5 computers per hour.
4 .18 1 .79
The average amount of money that people spend at Don Mcalds fast food place is $6.50 with a standard deviation of $1.75. 45 customers are randomly selected. Round all answers to two decimal places and assume a normal distribution. A. xBar~ N( , ) B. For the 45 customers, find the probability that their average spent is less than $5.00. C. What is the probability that one randomly selected customer will spend less than $5.00?
6.5 .26 0 .2
The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 10 mL. Suppose that 25 randomly selected people are observed pouring syrup on their pancakes. Round all answers to two decimal places. A. xBar~ N( , ) B. For the group of 25 pancake eaters, find the probability that the average amount of syrup is between 55 mL and 65 mL. C. If a single randomly selected individual is observed, find the probability that the this person consumes between 55 mL and 65 mL of syrup.
60 2 .99 .38
The average number of miles (in thousands) that a car's tire will function before needing replacement is 68 and the standard deviation is 15. Suppose that 9 randomly selected tires are tested. A. xBar~ N( , ) B. For the 9 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65 and 75 . C. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65 and 75 .
68 5 .64 .26
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.5 ppm and standard deviation 1.4 ppm. 18 randomly selected large cities are studied. Round all answers to two decimal places. A. xBar~ N( , ) B. For the 18 cities, find the probability that the average amount of pollutants is more than 9 ppm. C. What is the probability that one randomly selected city's waterway will have more than 9 ppm pollutants? D. Find the IQR for the average of 18 cities. Q1 = Q3 = IQR:
8.5 .33 .06 .36 8.28 8.72 .45
54% of students entering four-year colleges receive a degree within six years. Is this percent different for students who play intramural sports? 458 of the 800 students who played intramural sports received a degree within six years. H0: p = 0.54
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On average, Americans have lived in 3 places by the time they are 18 years old. Is this average less for college students? The 67 randomly selected college students who answered the survey question had lived in an average of 2.6 places by the time they were 18 years old. The standard deviation for the survey group was 1.4. H0: u = 3
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The average salary for American college graduates is $46,000. You suspect that the average is less for graduates from your college. The 43 randomly selected graduates from your college had an average salary of $44,519 and a standard deviation of $14,692. What can be concluded at the 0.05 level of significance? H0: u = 46000
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American college students have an average of 4.6 credit cards per student. Is the average more for 20-year-olds who are not in college? The data for the 19 randomly selected 20-year-olds who are not in college is shown below: 8, 4, 3, 0, 6, 2, 4, 11, 5, 5, 4, 2, 3 ,4, 2, 7, 4, 9, 7 H0: u = 4.6
>
The average amount of time it takes for couples to further communicate with each other after their first date has ended is 1.5 days. The standard deviation is 0.6 days. Is this average longer for blind dates? A researcher interviewed 34 couples who had recently been on blind dates and found that they averaged 1.65 days to communicate with each other after the date was over. H0: u = 1.5 Ha: u Not Equal 1.5
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The average salary for American college graduates is $46,000. You suspect that the average is more for graduates from your college. The 47 randomly selected graduates from your college had an average salary of $53,115 and a standard deviation of $24,197. What can be concluded at the 0.1 level of significance? H0: u = 46000
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The symbol O-x represents the population standard deviation of all possible sample means from samples of size n.
True
If a researcher wants to have a distribution of a sample that is approximately normal then that researcher should collect a sample with sample size greater than 30.
False
The symbol O^p represents the standard deviation of all possible sample proportions from samples of size n.
True
A larger sample size will result in a smaller sample standard deviation.
False
Convenience sampling was used to ask 20 students how much money they spent on books this quarter. The standard deviation was found to be $35. If a larger sample with a more scientific sampling technique is used then the standard deviation of the new sample will go down.
False
If the distribution of the population has a nonzero standard deviation and mean 10 then the probability that an individual data value will be greater than 11 is always less than the probability that the mean of 25 randomly selected data values will be greater than 11.
False
The symbol O-x represents the standard deviation of a sample of size n.
False
The symbol U-x represents the mean of a sample of size n.
False
The symbol U^p represents the proportion of a sample of size n.
False
Currently patrons at the library speak at an average of 63.2 decibels and the standard deviation is 4 decibels. Will this average increase after a "keep your voices down" sign is removed from the front entrance? After the sign was removed, the librarian random recorded 41 patrons speaking at the library. Their average decibel level was 64.1. H0: u = 63.2 Ha: u < 64
Not Equal
The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if there will be a difference in the average final exam score for students who are given colored pens on the first day of class. The final exam scores for the 18 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 88, 84, 68, 96, 72, 81, 97, 77, 79, 85, 81, 52, 80, 98, 83, 78, 90 What can be concluded at the 0.05 level of significance? H0: u = 77
Not Equal
If a distribution is skewed right, then the median for this population is smaller than the median for the sampling distribution with sample size 100.
True
If the sample size is 100 and the population standard deviation is 20, then the standard deviation of the sampling distribution is 2.
True
The population mean will always be the same as the mean of all possible x-bars that can be computed from samples of size 200.
True
54% of students entering four-year colleges receive a degree within six years. Is this percent different for students who play intramural sports? 458 of the 800 students who played intramural sports received a degree within six years. H0: p = 0.54 Ha: p < 0.54
not equal
Before the furniture store began its ad campaign, it averaged 166 customers per day. The manager is hoping that the average has changed since the ad came out. The data for the 10 randomly selected days since the ad campaign began is shown below: 179, 182, 150, 203, 145, 199, 182, 234, 200, 177 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? H0: u = 166
not equal