Math
If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 8, n2 = 8, the degrees of freedom for the tstatistic is ________.
7
The standard deviation of all possible sample proportions increases as the sample size increases.
False
The dependent variable is the variable that is being described or predicted.
True
The correlation coefficient may assume any value between
-1 and 1
The chief chemist for a major gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.3 ounces of this certain ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline?
.0062
In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. What is σx⎯⎯σx¯ ?
.0166
A random sample of size 1,000 is taken from a population where p = .20. What is μpˆμp^ ?
.20
In a manufacturing process a random sample of 9 manufactured bolts has a mean length of 3 inches with a standard deviation of .3 inches and is normally distributed. What is the 95 percent confidence interval for the true mean length of the manufactured bolt?
2.769 to 3.231
The χ2 statistic from a contingency table with 6 rows and 5 columns will have
20 degrees of freedom.
You want to estimate the proportion of customers who are satisfied with their experiences at a local supermarket at α = .10 and within .025 of the true value. It has been estimated that p =.85. How large of a sample is needed?
553
In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Past data indicate that the standard deviation is .25 inches. How many manufactured bolts should be sampled in order to make us 95 percent confident that the sample mean bolt length is within .02 inches of the true mean bolt length?
601
According to a hospital administrator, historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients was conducted. What is the probability that at least 70 patients will not be satisfied with the after-surgery care?
89.44%
If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 10, n2 = 10, the degrees of freedom for the t statistic is ________.
9
The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent). The historical records of the company show that over the past 8 years, the average has been that 13 percent of the accounts have been delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent?
92.08%
A null hypothesis is not rejected at a given level of significance. As the assumed value of the mean gets further away from the true population mean, the Type II error will ________.
Decrease
A confidence interval for the population mean is meant to contain a specified percentage of the individual population measurements.
False
A fastener manufacturing company uses a chi-square goodness-of-fit test to determine if a population of all lengths of ¼-inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is approximately normally distributed.
False
A sample size of 500 is sufficiently large to conclude that the sampling distribution of pˆp^ is a normal distribution, when the estimate of the population proportion is .995.
False
Expected cell frequencies for a multinomial distribution are calculated by assuming statistical dependence.
False
T or F: Alpha (α) is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.
False
T or F: In forming a confidence interval for μ1 − μ2, only two assumptions are required: independent samples and sample sizes of at least 30.
False
T or F: In testing the difference between the means of two independent populations, if neither population is normally distributed, then the sampling distribution of the difference in means will be approximately normal, provided that the sum of the sample sizes obtained from the two populations is at least 30.
False
T or F: The larger the p-value, the more we doubt the null hypothesis.
False
T or F:In testing the difference between the means of two normally distributed populations using independent random samples, the alternative hypothesis always indicates no difference between the two specified means.
False
The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.
False
A manufacturing company produces part QV2Y for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part QV2Y is the same for all three processes. The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and Process 3 manufactured 9 defective units in 150 items. At a significance level of 0.05, we performed a chi-square test to determine whether the quality of the items produced appears to be the same for all three processes. What is the null hypothesis
H0: The number of defectives produced is independent of the production process used.
As standard deviation increases, sample size ________ to achieve a specified level of confidence.
Increases
In determining the sample size to estimate a population proportion, as p approaches .5, the calculated value of the sample size ________.
Increases
An experiment in which there is no relationship between the measurements on the different samples is a(n) ________ experiment.
Independent samples
For a fixed sample size, what happens to a confidence interval for μ when we increase the level of confidence?
It gets wider
The Central Limit Theorem states that as the sample size increases, the distribution of the sample ________ approaches the normal distribution.
Means
In comparing the difference between two independent population means, the sampling distributions of the population means are at least approximately ________.
Normal
The spread of the sampling distribution of x⎯⎯x¯ is ________ the spread of the corresponding population distribution sampling distribution.
Smaller than
In a contingency table, when all the expected frequencies equal the observed frequencies, the calculated χ2 statistic equals zero.
True
In simple regression analysis, r2 is a percentage measure and measures the proportion of the variation explained by the simple linear regression model.
True
T or F: A Type I error is rejecting a true null hypothesis.
True
T or F: An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.
True
T or F: As the level of significance, α, increases, we are more likely to reject the null hypothesis.
True
T or F: Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Therefore, one way of expressing the null hypothesis is H0: μ = 100.
True
T or F: The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2. The weekly sales are normally distributed. This problem should be analyzed using an independent means method.
True
The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
True
The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.
True
The simple coefficient of determination is the proportion of total variation explained by the regression line.
True
The test of means for two related populations matches the observations (matched pairs) in order to reduce the ________ attributable to the difference between individual observations and other factors.
Variation
The tolerance interval of 95.44 percent is ________ a 95.44 percent confidence interval.
Wider than
When testing the difference between two population proportions using large independent random samples, the ________ test statistic is used.
Z
The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Find the interval that contains 95.44 percent of the sample means. rev: 11_06_2020_QC_CS-240046
[5.04, 5.36]
In a simple linear regression model, the slope term is the change in the mean value of y associated with ________ in x.
a one-unit increase
Assuming the same level of significance α, as the sample size increases, the value of tα/2 ________ approaches the value of zα/2.
always
In testing for the equality of means from two independent populations, if the hypothesis of equal population means is rejected at α = .01, it will ________ be rejected at α = .05.
always
As the Type II error, β, of a statistical test increases, the power of the test ________.
decreases
A Type II error is defined as ________ H0, when it should ________.
failing to reject, be rejected
In simple linear regression analysis, if the error terms exhibit a positive or negative autocorrelation over time, then the assumption of constant variance is violated.
false
The ________ the r2 and the ________ the s (standard error), the stronger the relationship between the dependent variable and the independent variable.
higher, lower
A special version of the chi-square goodness-of-fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for ________.
homogeneity
While a binomial distribution describes count data that can be classified into one of two mutually exclusive categories, a ________ distribution describes count data that are classified into more than two mutually exclusive categories.
multinomial
When the level of confidence and the sample size remain the same, a confidence interval for a population mean μ will be ________ when the sample standard deviation s is small than when s is large.
narrower
For a given hypothesis test, if we do not reject H0, and H0 is true,
no error has been committed
In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the
slope of the regression line.
After plotting the data points on a scatter diagram, we have observed an inverse relationship between the independent variable (X) and the dependent variable (Y). Therefore, we can expect both the sample ________ and the sample ________ to be negative values.
slope, correlation coefficient
Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ________ be rejected at the same significance level.
sometimes
Using the p-value rule, if a null hypothesis is rejected at a significance level of .05, it will ________ be rejected at a significance level of .01
sometimes
When testing the difference between two population proportions, the ________ test statistic is used.
z
The t distribution approaches the ________ distribution as the sample size ________.
z, increases
For large samples, the sampling distribution of x⎯⎯x¯ is approximately normal with a mean of ________.
μ
The range for r2 is between 0 and 1, and the range for r is between ________.
−1 and 1
Congratulations! You have just won the question-and-answer portion of a popular game show and will now be given an opportunity to select a grand prize. The game show host shows you a large revolving drum containing four identical white envelopes that have been thoroughly mixed in the drum. Each of the envelopes contains one of four checks made out for grand prizes of 20, 40, 60, and 80 thousand dollars. Usually, a contestant reaches into the drum, selects an envelope, and receives the grand prize in the envelope. Tonight, however, is a special night. You will be given the choice of either selecting one envelope or selecting 2 envelopes and receiving the average of the grand prizes in the two envelopes. If you select one envelope, the probability is 1/4 that you will receive any one of the individual grand prizes 20, 40, 60, and 80 thousand dollars. Assume you select two envelopes. There are six combinations, or samples, of two grand prizes that can be randomly selected from the four grand prizes 20, 40, 60, and 80 thousand dollars. Four of these samples are (60, 80), (20, 80), (20, 40), and (40, 80). Select the other two samples.
(40, 60) & (20, 60)
A random sample of size 1000 is taken from a population where p=.20, what is u^p?
.20
Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.
.8033
A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is σx⎯⎯σx¯ ?
.833
A random sample size of 36 is taken from a population with a mean 50 and standard deviation 5. What is population mean ( symbol )
.833
It has been reported that the average time to download the home page from a government website was .9 seconds. Suppose that the download times were normally distributed with a standard deviation of .3 seconds. If random samples of 36 download times are selected, calculate the mean of the sampling distribution of the sampling mean.
.9
The χ2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 observations and is divided into 6 categories (intervals). The degrees of freedom for the chi-square statistic are
3
On a standard IQ test, the standard deviation is 15. How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of .5) and we want 97 percent confidence in the results?
4,239
If the sampled population has a mean of 48 and standard deviation of 16, then respectively the mean and the standard deviation for the sampling distribution of x⎯⎯x¯ for n = 16 are
48 and 4.
A researcher for a paint company is measuring the level of a certain chemical contained in a particular type of paint. If the paint contains too much of this chemical, the quality of the paint will be compromised. On average, each can of paint contains 10 percent of the chemical. How many cans of paint should the sample contain if the researcher wants to be 98 percent certain of being within 1 percent of the true proportion of this chemical?
4870
In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process, what is the probability the mean length of the bolt is at least 3.16 inches?
5.48%
In a simple linear regression analysis, the correlation coefficient (r) and the slope (b) ________ have the same sign.
Always
In a simple regression analysis for a given data set, if the null hypothesis β = 0 is rejected, then the null hypothesis ρ = 0 is also rejected. This statement is ________ true.
Always
For any sampled population, the population of all sample means is approximately normally distributed.
False
For any samples population, the population of all sample means is approximately normally distributed.
False
If p = .9 and n = 40, then we can conclude that the sampling distribution of pˆp^ is approximately a normal distribution.
False
In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between the independent and dependent variables, but also shows whether the relationship is positive or negative
False
T or F:There are two types of machines, called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the 15 workers to both types of machines to compare their hourly production rate. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.
False
The chi-square goodness-of-fit test can only be used to test whether a population has specified multinomial probabilities or to test if a sample has been selected from a normally distributed population. It cannot be used if sample data come from other distribution forms, such as the Poisson.
False
When determining the sample size (n) for a confidence interval for ρ, if past experience tells us that p is at least .8, use p = .2.
False
When determining the sample size, n, if the value found for n is 79.2, we would choose to sample 79 observations.
False
When the level of confidence and sample size remain the same, a confidence interval for a population proportion, p, will be narrower when pˆ(1−pˆ)p^(1−p^) is larger than when pˆ(1−pˆ)p^(1−p^) is smaller.
False
When using simple regression analysis, if there is a strong correlation between the independent and dependent variables, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.
False
A real estate company is analyzing the selling prices of residential homes in a given community. 140 homes that have been sold in the past month are randomly selected and their selling prices are recorded. The statistician working on the project has stated that in order to perform various statistical tests, the data must be distributed according to a normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the statistician divides the data into 6 classes of equal size and records the number of observations in each class. She then performs a chi-square goodness-of-fit test for normal distribution. The results are summarized in the following table.
H0: The residential home selling prices are distributed according to a normal distribution.
An experiment in which two different measurements are taken on the same units and inferences are made using the differences between the pairs of measurements is a(n) ________ experiment.
Paired difference
In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels, the cholesterol levels of 9 heart patients are measured before they are given the drug. The same 9 patients use XZR for two continuous months. After two months of continuous use, the cholesterol levels are measured again. The comparison of cholesterol levels before versus after the administration of the drug is an example of testing the difference between two ________.
Paired samples
A manufacturing company produces part QV2Y for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part QV2Y is the same for all three processes. The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and Process 3 manufactured 9 defective units in 150 items. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used. What is the rejection point condition?
Reject H0 if χ2 > 5.99147
In performing a chi-square goodness-of-fit test with multinomial probabilities, the ________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are favored over the alternative hypothesis.
Smaller
When comparing two independent population means by using samples selected from two independent, normally distributed populations with equal variances, the correct test statistic to use is ________.
T
In testing the difference between the means of two independent populations, the variances of the two samples can be pooled if the population variances are assumed to ________.
To be equal
A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.
True
Assuming the same level of significance α, as the sample size increases, the value of tα/2 approaches the value of zα/2.
True
T or F: The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .045 for the test. If the significance level (α) for this test is .05, the null hypothesis would be rejected.
True
T or F: When applying either the critical value rule or the p-value rule about a single mean, other relevant factors held constant, increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type II error.
True
T or F: When the null hypothesis is not rejected, there is no possibility of making a Type I error.
True
T or F: When we are testing a hypothesis about the difference in two population proportions based on large independent samples, we compute a combined (pooled) proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.
True
T or F: You cannot make a Type II error when the null hypothesis is true.
True
The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).
True
When using a chi-square goodness-of-fit test with multinomial probabilities, the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.
True
When we carry out a chi-square test of independence, if ri is the row total for row i and cj is the column total for column j, then the estimated expected cell frequency corresponding to row i and column j equals (ri)(cj)/n.
True
The width of a confidence interval will be
Wider for a 99% confidence than for 95% confidence
When the level of confidence and sample proportion pˆp^ remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be ________ a confidence interval for p based on a sample of n = 400.
Wider than
A sample of 2,000 people yielded p⎯⎯p¯ = .52. Calculate a 90 percent confidence interval for p.
[.502, .538]
A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of .996 ounces with a standard deviation of .004 ounces. Construct a 98 percent confidence interval for the mean weight of all such candy.
[.9940, .9980]
A sample of 100 items has a population standard deviation of 5.1 and a mean of 21.6. Construct a 95 percent confidence interval for μ.
[20.60, 22.60]
In a study of factors affecting whether soldiers decide to reenlist, 320 subjects were measured for an index of satisfaction. The sample mean is 28.8 and the sample standard deviation is 7.3. Use the given sample data to construct the 98 percent confidence interval for the population mean for level of satisfaction.
[27.85, 29.75]
The strength of the relationship between two quantitative variables can be measured by
both the coefficient of correlation and the coefficient of determination.
As the sample size ________, the variation of the sampling distribution of x⎯⎯x¯ ________.
increases, decreases
When the assumption of ________ residuals (error terms) is violated, the Durbin-Watson statistic is used to test to determine if there is significant ________ among the residuals.
independent, autocorrelation
A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5. The sampling distribution of x⎯⎯x¯ ________.
is approximately normal
A real estate company is analyzing the selling prices of residential homes in a given community. 140 homes that have been sold in the past month are randomly selected and their selling prices are recorded. The statistician working on the project has stated that in order to perform various statistical tests, the data must be distributed according to a normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the statistician divides the data into 6 classes of equal size and records the number of observations in each class. She then performs a chi-square goodness-of-fit test for normal distribution. The results are summarized in the following table.
reject H0; conclude that the residential home selling prices are not distributed according to a normal distribution.
The least squares regression line minimizes the sum of the
squared differences between actual and predicted Y values.
When testing the difference for the population of paired differences in which two different observations are taken on the same units, the correct test statistic to use is ________.
t
In testing the difference between the means of two normally distributed populations using independent random samples with equal variances, the correct test statistic to use is the
t statistic
A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as ________.
the Central Limit Theorem
