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 .

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Answer 1

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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.

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PS 9 Two films are shown on screen A and screen B at a cinema each evening. The numbers of people viewing the films on 12 consecutive evenings are shown in the back-to-back stem-and-leaf diagram. Screen A (12) Screen B (12) 8 037 34 7 6 4 0 534 74 1645678 92 71689 Key: 116|4 represents 61 viewers for A and 64 viewers for B A second stem-and-leaf diagram (with rows of the same width as the previous diagram) is drawn showing the total number of people viewing films at the cinema on each of these 12 evenings. Find the least and greatest possible number of rows that this second diagram could have. TIP On the evening when 30 people viewed films on screen A, there could have been as few as 37 or as many as 79 people viewing films on screen B.

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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.

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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.

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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.

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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 .

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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.

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