You would like to construct a 99% confidence interval to estimate today's population mean temperature, so you make a series of measurements (a random sample) throughout the day. The mean of these measurements is 58.5 degrees Fahrenheit, and their standard deviation is 3.0 degrees Fahrenheit. For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)

You would like to construct a 99% confidence interval to estimate today's population mean temperature, so you make a series of measurements (a random sample) throughout the day. The mean of these measurements is 58.5 degrees Fahrenheit, and their standard deviation is 3.0 degrees Fahrenheit. For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)

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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Question

100%

For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)

Sampling scenario
The sample has size 95, and it is from a non-normally
distributed population.
The sample has size 14, and it is from a normally distributed
population with an unknown standard deviation.
The sample has size 12, and it is from a normally distributed
population with a known standard deviation of 3.
N
O
O
O
t
O
O
O
Could use
either Z or t
O
Unclear

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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