Suppose that you want to estimate the mean annual income for people over age 40 in your state. You choose a random sample of such incomes and compute the mean of the sample as 40418.5 dollars with a standard deviation of 7481 dollars. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.(In the table, Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution.) Sampling ScenarioZtcould use either Z or tunclear(1) The sample has size 80, and it is from a non-normally distributed population. (2) The sample has size 20, and it is from a population with a distribution about which we know very little. (3) The sample has size 15, and it is from a normally distributed population with unknown standard deviation. (4) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 7549. (5) The sample has size 18, and it is from a normally distributed population with a known standard deviation of 7549.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Suppose that you want to estimate the mean annual income for people over age

in your state. You choose a random sample of such incomes and compute the mean of the sample as

40418.5

dollars with a standard deviation of

7481

dollars. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

(In the table,

refers to a variable having a standard normal distribution, and

refers to a variable having a t distribution.)

Sampling Scenario	Z	t	could use either Z or t	unclear
(1) The sample has size 80, and it is from a non-normally distributed population.
(2) The sample has size 20, and it is from a population with a distribution about which we know very little.
(3) The sample has size 15, and it is from a normally distributed population with unknown standard deviation.
(4) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 7549.
(5) The sample has size 18, and it is from a normally distributed population with a known standard deviation of 7549.

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.

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