Stats Test #2
A company has developed a new diet that it claims will lower one's weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The manager of the company __________.
is more concerned about Type II error
The finite correction factor is always ______
less than one, and therefore decreases the standard deviations of X¯ and P¯ computed under the assumption of infinite population
In general, the null and alternative hypotheses are __________.
mutually exclusive
Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.
n = 73
Under what condition is the finite population correction factor used for computing the standard error of X¯ and P¯
n ≥ 0.05N
A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval?
833
Which of the following is correct
A continuous random variable has a probability density function, and a discrete random variable has a probability mass function
Which of the following meets the requirements of a cluster sample?
A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks
Which of the following meets the requirements of a simple random sample?
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age
The cumulative distribution function is denoted and defined as which of the following?
F(x) and F(x) = P(X ≤ x)
Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim.
H0: p ≥ 0.84 and HA: p < 0.84
Which of the following are two-tailed tests?
H0:μ = 10, HA:μ ≠ 10
The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. To determine whether there has been a decrease in the average number of customers visiting the dealership daily, the appropriate hypotheses are __________.
H0:μ≥800,HA:μ<800H0:μ≥800,HA:μ<800
For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?
If the population standard deviation is greater, the interval is wider.
Which of the following is the necessary condition for creating confidence intervals for the population mean?
Normality of the estimator
It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X < 20) related to P(X < 16)?
P(X < 20) is greater than P(X < 16).
Which of the following is the assumption that is not applicable for a one-way ANOVA test?
The population standard deviations are not all equal.
Which of the following statements is FALSE regarding the given curves showing the shapes of a probability density function for different values of a key parameter λ?
The red curve has the lowest value of the rate parameter λ
What is the purpose of calculating a confidence interval?
To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.
The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval?
np⎯⎯≥5n p¯ ≥ 5 and n(1−p⎯⎯)≥5n ( 1 − p¯) ≥ 5
For a categorical variable, the most appropriate control chart to monitor the proportion of a certain characteristic is a(n)
p¯ chart.
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to __________.
reject the null hypothesis
In order to increase participation, survey respondents will enter for a chance to win one of fifty $10 gift cards upon completion of the survey. There are 785 survey respondents. Which of the following is R's function to generate a simple random sample of fifty gift card winners?
sample(1:785, 50)
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ 0.50 and HA: p > 0.50, p stands for __________.
the current proportion of babies born out of wedlock
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then __________
the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been _________
wider; smaller
For a numerical variable, the most appropriate control chart to monitor central tendency is a(n)
x¯ chart.
Find the z value such that P(Z ≤ z) = 0.9082
z = 1.33
A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 8 minutes. A random sample of 60 employees were selected and they averaged 8.6 minutes. It is believed that the population standard deviation is 2.3 minutes. The α is set to 0.05. The p-value for this hypothesis test would be __________.
0.0217
The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take more than five hours to construct a soapbox derby car.
0.0228
The probability P(Z < −1.28) is closest to
0.10
A random sample of 120 cast aluminum pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.05. What are the upper and lower control limits for the p¯ chart?
0.1097 and 0.0
On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. What is the probability that the appliance will work at least six years without requiring repairs?
0.2231
Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that from the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait less than two minutes?
0.3333
Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon. What is the probability a randomly chosen gas station charges between $3.70 and $3.90 per gallon?
0.3333
Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate p^ of the population proportion, what value should be assumed for p^ ?
0.50
Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be between $325 and $425?
0.5275
You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough?
0.7734
The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 14.2 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
0.9192
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean?
1.96(3.20/6)
If an exponential distribution has the rate parameter λ = 5, what is its expected value?
1/5
A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius. Inspectors take weekly samples for 5 weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below. Week 1 4.97 Week 2 5.16 Week 3 5.12 Week 4 5.35 Week 5 5.50 How many points are outside the control limits?
2
A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius. Inspectors take weekly samples for 5 weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below. Week 1 5.60 Week 2 5.40 Week 3 4.93 Week 4 4.98 Week 5 4.82 How many points are outside the control limits?
2
Sixty percent of 800 students in a Business Statistics class are female. If you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, what minimal sample size of the random sample should be used?
40
The finite population correction factor for the standard error of the mean should be used when the ratio of the sample size to the size of population exceeds ______
5%
Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ______.
50% chance that the actual return will be greater than 8%
The following is an incomplete ANOVA table. Source of Variation SS df MS F Between groups 2 12.5 Within groups Total100 10 For the within groups category, the degrees of freedom are _______.
8
Which of the following meets the requirements of a stratified random sample?
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25
Which of the following are one-tailed tests?
Both H0:μ ≤ 10, HA:μ > 10 and H0:μ ≥ 400, HA:μ < 400
A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university's belief, how does one define the population parameter of interest?
It's the proportion of honors graduates with a GPA of 3.00 or below.
John would like to conduct a survey in his neighborhood to get homeowners' opinion on the Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample?
John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group
Peggy would like to conduct a survey in her neighborhood to get homeowners' opinions on the Delmarva proposal to switch to natural gas. Which of the following is an example of a convenience sample?
John selects the first 25 homes that he passes as he walks into the entrance of the development
Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $22.31 and a 95% confidence interval of [$20.5051, $24.2091]. Which of the following statements is a valid explanation of the confidence interval.
We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.
A random sample of 150 cast aluminum pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.04. The sample proportions for the week are shown in the accompanying table. Day of the Week Proportion, Defective Monday, 0.06 Tuesday, 0.07 Wednesday, 0.04 Thursday, 0.06 Friday, 0.05 Is the production process in control?
Yes, because the sample proportions fall within the upper and lower control limits
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $15,600. A random sample of 45 students had an average debt load of $16,800. It is believed that the population standard deviation for student debt load is $4,300. The α is set to 0.05. The confidence interval for this hypothesis test would be __________.
[$15,543.63, $18,056.37]
We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
[11.7019, 13.2981]
At an academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71. Develop a 90% confidence interval for the population mean GPA
[2.5261, 2.8939]
We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?
[25.8567, 28.1433]
Bob's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The 90% confidence interval around this sample mean is ______.
[92.4, 94.8]
In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to ______
a number of randomly occurring events that are part of the production process
Acceptance sampling is _______
an inspection of a portion of the products at the completion of the production process
The alternative hypothesis typically __________.
contests the status quo, for which a corrective action may be required
The detection approach to statistical quality control ______
determines at which point the production process does not conform to specifications
Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.64. If we choose a 1% significance level, then we __________.
do not reject the null hypothesis and conclude that the population mean is not significantly different from zero
Which of the following is not a characteristic of a probability density function f(x)?
f(x) is symmetric around the mean
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is __________.
z = 1.50
