Lecture Slides on Introduction to Statistical Analysis - Homework 10 | STAT 245, Assignments of Data Analysis & Statistical Methods

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Stat245 Recitation 18

TA: Dongmei Li

Nov. 20, 2007

Announcement and Outline

I (^) Homework 10 consists of the following exercises in Chapter 10: 10.6, 10.28, 10.42, 10.56, 10.64, 10.74, and 10.82.

I (^) Exam regrades are due in recitation on Tuesday of next week.

I (^) Exam 2 Review.

I (^) Review hypothesis test for population proportion.

I (^) Problem Solving (Chapter 10).

I (^) 1. T/F A random variable is continuous if the set of possible values includes an entire interval on the number line. I (^) Answer: True.

I (^) 1. T/F A random variable is continuous if the set of possible values includes an entire interval on the number line. I (^) Answer: True.

I (^) 2. T/F The distribution of all values of a random variable is called a normal distribution.

I (^) 1. T/F A random variable is continuous if the set of possible values includes an entire interval on the number line. I (^) Answer: True.

I (^) 2. T/F The distribution of all values of a random variable is called a normal distribution. I (^) Answer: False, because only random variable that follows a symmetric, bell-shaped curve is said to have a normal distribution.

I (^) 3. T/F For every random variable, P(a ≤ x ≤ b) = P(a < x < b).

I (^) 1. T/F A random variable is continuous if the set of possible values includes an entire interval on the number line. I (^) Answer: True.

I (^) 2. T/F The distribution of all values of a random variable is called a normal distribution. I (^) Answer: False, because only random variable that follows a symmetric, bell-shaped curve is said to have a normal distribution.

I (^) 3. T/F For every random variable, P(a ≤ x ≤ b) = P(a < x < b). I (^) Answer: False, because it is only valid when x is a continuous random variable.

I (^) 4. T/F A statistic is a characteristic of the population.

I (^) Answer: False, because a statistic is a characteristic of the sample.

I (^) 4. T/F A statistic is a characteristic of the population.

I (^) Answer: False, because a statistic is a characteristic of the sample.

I (^) 5. T/F The standard deviation of the distribution of ¯x decreases as n increases.

I (^) 4. T/F A statistic is a characteristic of the population.

I (^) Answer: False, because a statistic is a characteristic of the sample.

I (^) 5. T/F The standard deviation of the distribution of ¯x decreases as n increases. I (^) Answer: True, because σ¯x = √σn (With n increase, σ¯x will

decrease.)

I (^) 6. T/F The sampling distribution of p tends to be more spread out for larger sample sizes than for smaller sample sizes.

I (^) 4. T/F A statistic is a characteristic of the population.

I (^) Answer: False, because a statistic is a characteristic of the sample.

I (^) 5. T/F The standard deviation of the distribution of ¯x decreases as n increases. I (^) Answer: True, because σ¯x = √σn (With n increase, σ¯x will

decrease.)

I (^) 6. T/F The sampling distribution of p tends to be more spread out for larger sample sizes than for smaller sample sizes.

I (^) Answer: False, because σp =

π(1−π) n (When^ n^ is large,^ σp will be small).

I (^) 7. T/F The distribution of ¯x is normal if the population is normal.

I (^) Answer: True, because the distribution of ¯x is always normal when the population has normal distribution.

I (^) 7. T/F The distribution of ¯x is normal if the population is normal.

I (^) Answer: True, because the distribution of ¯x is always normal when the population has normal distribution.

I (^) 8. T/F The distribution of ¯x will always have the same shape as the distribution of the population being sampled.

I (^) 7. T/F The distribution of ¯x is normal if the population is normal.

I (^) Answer: True, because the distribution of ¯x is always normal when the population has normal distribution.

I (^) 8. T/F The distribution of ¯x will always have the same shape as the distribution of the population being sampled. I (^) Answer: False, because When sample size is large (n > 30) the distribution of ¯x is will be normal even when the population does not has normal distribution.

I (^) 9. T/F The closer π is to 0 or 1, the larger n must be in order for the distribution of p to be approximately normal.

I (^) 7. T/F The distribution of ¯x is normal if the population is normal.

I (^) Answer: True, because the distribution of ¯x is always normal when the population has normal distribution.

I (^) 8. T/F The distribution of ¯x will always have the same shape as the distribution of the population being sampled. I (^) Answer: False, because When sample size is large (n > 30) the distribution of ¯x is will be normal even when the population does not has normal distribution.

I (^) 9. T/F The closer π is to 0 or 1, the larger n must be in order for the distribution of p to be approximately normal. I (^) Answer: True, because we need have nπ ≥ 10 and n(1 − π) ≥ 10 (n must be large when π is close to 0 or 1).