Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ 1 − μ 2 .

Question

Want to see more full solutions like this?

Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output: Estimate SE Z Pr(>|Z|) (Intercept) -0.8161 0.086 -9.4895 0 to_multiple -2.5651 0.3052 -8.4047 0 winner 1.5801 0.3156 5.0067 0 format -0.1528 0.1136 -1.3451 0.1786 re_subj -2.8401 0.363 -7.824 0 (a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…

Consider an event X comprised of three outcomes whose probabilities are 9/18, 1/18,and 6/18. Compute the probability of the complement of the event. Question content area bottom Part 1 A.1/2 B.2/18 C.16/18 D.16/3

John and Mike were offered mints. What is the probability that at least John or Mike would respond favorably? (Hint: Use the classical definition.) Question content area bottom Part 1 A.1/2 B.3/4 C.1/8 D.3/8

Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Answer 6

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Answer 7

Chapter 8, Problem 1CRP

To determine

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Answer 8

Expert Solution & Answer

Explanation of Solution

If the population x distribution is normal with known population standard deviation (σ) or if sample size is n≥30 with known population standard deviation then the standard normal distribution must be used for testing μ or the difference of means μ1−μ2.

If the population x distribution is mounded shape, symmetric with unknown population standard deviation (σ) or if sample size is n≥30 with unknown population standard deviation then the Student’s t distribution with corresponding degrees of freedom must be used for testing μ or the difference of means μ1−μ2.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ 1 − μ 2 .

Concept explainers

Videos

Explain how to identify whether to use standard normal distribution or a Student’s t distribution for testing μ or the difference of means μ1−μ2.

Explanation of Solution

Want to see more full solutions like this?

Chapter 8 Solutions