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BANA 3363 - Unit 4

Terms in this set (82)

A confidence interval for the difference in means that does not contain 0, confirms the fact that the two population means are not equal.
True
SHSU would like to test whether there is any difference in salaries for business professors (group 1) and criminal justice professors (group 2). The university randomly selects a sample of 48 business professors and finds their average salary to be $82,628. The university also selects a random sample of 53 criminal justice professors and finds their average salary is $70,784. The population standard deviations are known and equal to $9000 for business professors, respectively $7500 for criminal justice professors. The university wants to test if there is a difference between the salaries of these 2 groups, using a significance level of 5%.
7.143
A food supplements company is conducting a study regarding the efficacy of one of their weight loss products. The company constructs a 95% confidence interval of the weight difference between users and non-users of this product and finds this difference lies between -2.3 lbs. and 4.1 lbs. This result
.
is not good proof that their product helps with weight loss.
If the sampling is done correctly, the sample mean difference is an unbiased estimator of the population mean difference.
True
For an alternative hypothesis of the form H1: μ1 - μ2 ≠ 0, a two-tail hypothesis test needs to be employed.
True
Which one of the following is true about hypotheses tests for comparing two population means?
Both one tail tests and two tails tests are possible to be specified and tested.
To test the efficacy of a hypertension drug, medical researchers sample the blood pressures of two different groups of people: one group that has been given a dose of the drug and one group that has been given a placebo. The resulting samples are called
Independent samples
Suppose that a drug manufacturer wants to test the efficacy of a hypertension drug. To do that they administer a dose of the drug to one group of people (group 1) and a placebo (a substance with no therapeutic effect) to another group of people (group 2). The company wants to prove that their drug lowers the blood pressure of patients. To prove this, the company needs to perform
a left tail test.
An R2 of 0.45 implies that 45% of the variance in the independent variable is explained by the dependent variable.
False
A simple linear regression has been performed to estimate the relationship between fuel efficiency (in miles per gallon) and engine size (in cubic liters). The regression results are displayed in the following table: What is the 95% upper confidence limit for the slope coefficient?
-1.6350
Which of the following results of a regression analysis implies that all data points fall exactly on the regression line?
SEE=0
A simple linear regression model will always have a single dependent variable, while a multiple regression model will have more than one dependent variables.
False
In a simple linear regression model, when SSE is equal to zero, SEE will also be equal to zero.
True
A simple linear regression has been performed to estimate the relationship between fuel efficiency (in miles per gallon) and engine size (in cubic liters). The regression results are displayed in the following table: What is the predicted value of fuel efficiency (in miles per gallon) for a car with a 2.5 cubic liters engine? Round your answer to two decimals, if needed.
25.92
The p-value for testing the significance of the regression slope has been found to be 0.045. Based on this, we are 95% confident that there is a relationship between the independent and dependent variables.
True
Using regression analysis, economists show that the wage that people earn depends on their age, education level, experience, and other factors. In such a regression model, the wage is called
the dependent variable.
In a simple linear regression model, if the standard error of the estimate is zero, this implies that
the regression model perfectly fits the data.
The OLS method
.
minimizes the sum of the squared residuals.
When performing hypothesis testing for multiple regression models,
statisticians can perform a T-test to test the individual significance of each regressor, and also can perform an F-test to test the overall significance of all regressors.
The adjusted R2 is always smaller than the unadjusted R2 and can never be negative.
false
A multiple regression has been performed to estimate the relationship between household heating bill (in dollars) and the house size (in square feet) and age of the heating system (in years). The regression results are displayed in the following table: What is the predicted heating bill for a 2500 square feet house with a 8 year old heating system? Round your answer to 2 decimals if needed.
Multiple regression equation is,
y=128.0107+0.0692House size + 4.3524Age
Substitute,
House size =2500
Age=8
=>y=128.0107+0.0692(2500) + 4.3524(8) = 335.83
A multiple regression has been performed to estimate the relationship between household heating bill (in dollars) and the house size (in square feet) and age of the heating system (in years). The regression results are displayed in the following table: What is the 95% upper confidence limit for the independent variable that is statistically significant at 10%?
P value for independent variable House size =0.0585 < 0.10
Upper limit for 95% confidence interval =0.1412
A slope parameter in a multiple regression model represents
the change in the dependent variable that is caused by a one unit change in the corresponding independent variable, when all other independent variables remain unchanged.
A multiple regression has been performed to estimate the relationship between people's credit scores and their age, weekly income, and years at their current residence. The regression results are displayed in the following table: What is the estimated slope coefficient for the independent variable that is statistically significant at 5%?
4.2166
If a t-test is performed in the context of a multiple regression model and the null hypothesis is rejected, this means that
the independent variable for which the test has been performed has a significant relationship with the dependent variable.
In the context of a multiple regression model, a regressor is
Any of the independent variables
A multiple regression model with 2 independent variables is estimated and the two slope coefficients are -1.04 and 2.34, This means that if both independent variables increase by 1 unit at the same time, the predicted value of the dependent variable will increase by 1.3.
True
The sampling distribution for the difference in means between two samples taken from two populations is normally distributed only if the original populations are normally distributed.
False
What is the predicted heating bill for a 2500 square feet house with a 8 year old heating system? Round your answer to 2 decimals if needed.
intercept + (coefficiant2500)+(coefficant8)
What is the residual for a car with a 4.2 cubic liters engine and a fuel efficiency of 16.56 mpg? Round your answer to two decimals, if needed.
intercept + (coefficiant*) - 2nd topic
A random sample of 5 students has been selected. Their overall GPAs are 2.5, 3.75, 2.36, 3.73, and 3.98. Calculate the sample mean GPA. Round up your answer to 2 decimals if needed.
3.264
Which one of the following descriptive statistics is a measure of spread?
A. The mean.
B. The mode.
C. The standard deviation.
D. The median.
Standard Deviation
If a t-test is performed in the context of a multiple regression model and the null hypothesis cannot be rejected, this means that

A. all independent variables have a significant relationship with the dependent variable.
B. no independent variable has a significant relationship with the dependent variable.
C. the independent variable for which the test has been performed has a significant relationship with the dependent variable.
D. the independent variable for which the test has been performed has no significant relationship with the dependent variable.
the independent variable for which the test has been performed has no significant relationship with the dependent variable.
We would like to construct a 95% confidence interval for the mean, based on a sample of 100 observations. The sample standard deviation is 3.5 and the sample mean is 12. The population standard deviation is 2.5. Calculate the upper confidence limit. Round your answer to 3 decimals if needed.
12.49
When performing a one-tail hypothesis test, a researcher found a critical value of -1.796 and a t-test statistic of -1.85. What is the correct conclusion of this test?

A. Reject the alternative hypothesis.
B. Reject the null hypothesis.
C. Support the null hypothesis.
D. Support the null hypothesis with 100% certainty.
Reject the null hypothesis.
A food supplements company is conducting a study regarding the efficacy of one of their weight loss products. The company constructs a 95% confidence interval of the weight difference between users and non-users of this product and finds this difference lies between -2.3 lbs. and 4.1 lbs. This result

A. is proof that their product will result in weight loss.
B. is proof that their product will actually lead to weight gain.
C. is not good proof that their product helps with weight loss.
D. is proof that their product does not have any effect.
is not good proof that their product helps with weight loss.
SHSU would like to construct a confidence interval for the difference in salaries for business professors (group 1) and criminal justice professors (group 2). The university randomly selects a sample of 52 business professors and finds their average salary to be $83,804. The university also selects a random sample of 49 criminal justice professors and finds their average salary is $66,761. The population standard deviations are known and equal to $9000 for business professors, respectively $7500 for criminal justice professors. The university wants to estimate the difference in salaries between the two groups by constructing a 95% confidence interval.
20,267
A simple linear regression model will always have a single independent variable, while a multiple regression model will have more than one independent variables
true
A company that produces light bulbs wants to test in their new LCD bulb has an average lifespan that exceeds 5000 hours. To support their claim they have collected a random sample of 68 bulbs and found the average lifespan of these 68 bulbs was 5071 hours. The population standard deviation is known to be 508 hours. The company would like to test their hypothesis using a significance level of 0.05. Calculate the appropriate p-value to test this hypothesis.
.12455
If an F-test is performed for a multiple regression model and the null hypothesis cannot be rejected, it means there is at least one regressor that is significant.
False
A random sample of 100 students has been selected from the population of SHSU students and two thirds of the sampled students were found to be females. Assuming the sampling was done correctly, this is a good

A. point estimate of the sample proportion of female students.
B. interval estimate of the sample proportion of female students.
C. point estimate of the population proportion of female students.
D. interval estimate of the population proportion of female students.
point estimate of the population proportion of female students.
Using regression analysis, economists show that the wage that people earn depends on their age, education level, experience, and other factors. In such a regression model, the wage is called

A. the right-hand side variable.
B. the regressor.
C. the independent variable.
D. the dependent variable.
the dependent variable.
A company that produces sports shoes claims that people wearing their running shoes can run a one mile in less than 5 minutes. To support their claim they have collected a random sample of 45 runners and found the average time it took these 45 runners to run a mile was 4.87 minutes. The standard deviation for this sample of runners was 0.2 minutes. The company would like to test their hypothesis using a significance level of 0.05. The correctly stated hypotheses are:

A. H0: μ ≤ 5 and H1: μ > 5
B. H0: μ ≥ 5 and H1: μ < 5
C. H0: μ > 5 and H1: μ < 5
D. H0: μ = 5 and H1: μ > 5
H0: μ ≥ 5 and H1: μ < 5
In 2010, the US Census has found that 25% of American households had a person 65 years or older living in them. The government would like to test if this proportion has increased since then. To achieve that, a random sample of 214 American household has been chosen, among which 82 households had a person 65 years or older living in them. Calculate the appropriate test statistic needed to test this hypothesis at a 0.1 level of significance.
4.50
The standard deviation is a measure describing the variability of data.
true
A t-distribution with a very high degrees of freedom is practically identical with a normal distribution.
true
The normal probability distribution is also referred to as the

A. standard distribution.
B. uniform distribution.
C. symmetric curve.
D. bell curve.
bell curve.
The standard normal distribution

A. has asymmetric tails.
B. has a variance of 0.
C. has a standard deviation of 1.
D. has a mean of 1.
has a standard deviation of 1.
Which one of the following is not a characteristic of the normal distribution?
A. The normal distribution is bell-shaped.
B. The normal distribution is symmetric around the mean.
C. The normal distribution always has a mean of 0.
D. The mean, mode, and median are the same for a normal distribution.
The mean, mode, and median are the same for a normal distribution.
Which one of the following is true?
A. As the sample size increases, the standard error of the mean decreases.
B. As the sample size increases, the standard error of the mean increases as well.
C. As the sample size increases, the population standard deviation decreases.
D. As the sample size increases, the population standard deviation increases.
As the sample size increases, the standard error of the mean decreases.
The standard deviation for a sample of 5 observations is 7.32. Calculate the variance. Round your answer to 2 decimals if needed.
53.58
3 randomly selected members of a large family have the following ages: 45, 23, and 46. Calculate the sample variance of age. Round your answer to 2 decimals if needed.
169
For a normally distributed population, we need a sample size of at least 30 for the sampling distribution to also be normal.
false
Inferential statistics can estimate the population mean, based on the sample mean.
True
Regardless of the shape of the population distribution, as the sample size increases, the sampling distribution becomes more and more bell-shaped.
True
If sampling is done correctly, the mean of the sampling distribution is always equal to the population mean.
true
The degrees of freedom of the t-distribution for calculating a confidence interval for the mean when the population standard deviation is unknown is equal to the sample size.
False
The larger the population standard deviation, the wider the confidence interval will be.
True
The significance level is the probability that the interval estimate will contain the population parameter of interest.
false
Based on a random sample of 50 Ford trucks, statisticians estimated that the average Ford truck on the American roads has a fuel efficiency of somewhere between 15 and 21 miles per gallon. Assuming the sampling was done correctly, this is a good

A. interval estimate of the population mean for the efficiency of Ford trucks.
B. point estimate of the population proportion of Ford trucks.
C. point estimate of the sample proportion of Ford trucks.
D. interval estimate of the sample mean for the efficiency of Ford trucks.
interval estimate of the population mean for the efficiency of Ford trucks.
To find the interval estimator,

A. we add the margin of error to the point estimator.
B. we add and subtract the margin of error from the point estimator.
C. we subtract the margin of error from the point estimator.
D. we double the point estimator.
we add and subtract the margin of error from the point estimator.
We would like to construct a 90% confidence interval for the mean, based on a sample of 35 observations. The sample standard deviation is 3.8 and the sample mean is 21. Calculate the upper confidence limit. Round your answer to 3 decimals if needed.
22.086
The margin of error for a confidence interval is larger if

A. the sample mean is larger.
B. the population mean is larger.
C. the sample size is larger.
D. the population standard deviation is larger.
the population standard deviation is larger.
Calculate the margin of error for an 80% confidence interval for the mean, when the sample size is 20, the sample mean is 35, and the sample standard deviation is 6.9. Round your answer to 3 decimals if needed.
2.049
We would like to construct a 99% confidence interval for the mean, based on a sample of 50 observations. The sample standard deviation is 5.5 and the sample mean is 22. The population standard deviation is 3.6. Calculate the lower confidence limit. Round your answer to 3 decimals if needed.
20.689
The z-score that corresponds to a probability of 0.0207 is -2.04
true
During a hypothesis test performed at the 0.05 significance level, a researcher found a p-value of 0.07. The correct conclusion of this hypothesis test would be to

A. Not reject the null hypothesis
B. Support the null hypothesis with 100% certainty
C. Support the alternative hypothesis
D. Reject the null hypothesis
Not reject the null hypothesis
n 2010, the US Census has found that 25% of American households had a person 65 years or older living in them. The government would like to test if this proportion has increased since then. To achieve that, a random sample of 265 American household has been chosen, among which 74 households had a person 65 years or older living in them. Calculate the p-value needed to test this hypothesis at a 0.1 level of significance.
0.1364
When performing a two tail hypothesis test for the population mean when the population standard deviation is unknown, how do we compute the degrees of freedom for the t-distribution?

A. We do not need to calculate the degrees of freedom for this test because we use the normal distribution instead.
B. The degrees of freedom equal the sample size.
C. The degrees of freedom equal the sample size minus 1.
D. The degrees of freedom equal the sample size minus 2.
The degrees of freedom equal the sample size minus 1.
A company that produces light bulbs wants to test in their new LCD bulb has an average lifespan that exceeds 5000 hours. To support their claim they have collected a random sample of 72 bulbs and found the average lifespan of these 72 bulbs was 5,132 hours. The population standard deviation is known to be 542 hours. The company would like to test their hypothesis using a significance level of 0.05. Calculate the appropriate test statistic.
2.07
For a fixed sample size, choosing a lower significance level will increase the probability of making a type II error.
True
Increasing the sample size reduces the probability of making a type I error, but increases the probability of making a type II error.
false
A food and beverage company wants to test if their new bottled vitamin supplement has an average content of 5000 mg of vitamin C. To support their claim they have collected a random sample of 83 bottles and found the average content of these 83 bottles was 5147 mg of vitamin C. The population standard deviation is known to be 488 mg. The company would like to test their hypothesis using a significance level of 0.05. Calculate the appropriate p-value to test this hypothesis.
0.0061439
Correct Answer: 0.0062
A company that produces light bulbs wants to test if their new LCD bulb has an average lifespan greater than 7500 hours. To support their claim they have collected a random sample of 79 bulbs and found the average lifespan of these 79 bulbs was 7600 hours. The population standard deviation is known to be 451 hours. The company would like to test their hypothesis using a significance level of 0.05. The correctly stated hypotheses are:

A. H0: μ ≤ 7500 and H1: μ > 7500
B. H0: μ = 7500 and H1: μ > 7500
C. H0: μ > 7500 and H1: μ < 7500
D. H0: μ ≥ 7500 and H1: μ < 7500
H0: μ ≤ 7500 and H1: μ > 7500
Which one of the following is a valid way to state a Null hypothesis about a population parameter X?

A. X>10
B. X=10
C. x<10
D. all of the above.
X=10
A p-value of 0.09 cannot reject a null hypothesis at a significance level of 10%.
False
SHSU would like to test whether there is any difference in salaries for business professors (group 1) and criminal justice professors (group 2). The university randomly selects a sample of 48 business professors and finds their average salary to be $82,628. The university also selects a random sample of 53 criminal justice professors and finds their average salary is $70,784. The population standard deviations are known and equal to $9000 for business professors, respectively $7500 for criminal justice professors. The university wants to test if there is a difference between the salaries of these 2 groups, using a significance level of 5%.
Compute the test statistic needed for performing this test. Round your answer to 2 decimals, if needed.
7.143
A food supplements company is conducting a study regarding the efficacy of one of their weight loss products. The company constructs a 95% confidence interval of the weight difference between users and non-users of this product and finds this difference lies between -2.3 lbs. and 4.1 lbs. This result

A. is proof that their product does not have any effect.
B. is not good proof that their product helps with weight loss.
C. is proof that their product will actually lead to weight gain.
D. is proof that their product will result in weight loss.
is not good proof that their product helps with weight loss.
SHSU would like to construct a confidence interval for the difference in salaries for business professors (group 1) and criminal justice professors (group 2). The university randomly selects a sample of 56 business professors and finds their average salary to be $76,846. The university also selects a random sample of 51 criminal justice professors and finds their average salary is $68,545. The population standard deviations are known and equal to $9000 for business professors, respectively $7500 for criminal justice professors. The university wants to estimate the difference in salaries between the two groups by constructing a 95% confidence interval.
Compute the upper confidence limit. Round your answer to 2 decimals, if needed.
11,430.48
Which one of the following is true about hypotheses tests for comparing two population means

A. Comparing two population means can only be done using a two tail test.
B. A two tail test is possible for comparing two population means, but only if the population standard deviations are known.
C. Both one tail tests and two tails tests are possible to be specified and tested.
D. Comparing two population means can only be done using a one tail test.
Both one tail tests and two tails tests are possible to be specified and tested.
To test the efficacy of a hypertension drug, medical researchers sample the blood pressures of two different groups of people: one group that has been given a dose of the drug and one group that has been given a placebo. The resulting samples are called

A. Non-random samples
B. Dependent samples
C. Independent samples
D. Normalized samples
Independent samples
Suppose that a drug manufacturer wants to test the efficacy of a hypertension drug. To do that they administer a dose of the drug to one group of people (group 1) and a placebo (a substance with no therapeutic effect) to another group of people (group 2). The company wants to prove that their drug lowers the blood pressure of patients. To prove this, the company needs to perform

A. a left tail test and a right tail test.
B. a right tail test.
C. a two tail test.
D. a left tail test.
a left tail test
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