Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample mean is 23.1 hours. There is a known population standard deviation of 6.6 hours. The population distribution is assumed to be normal.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a)Find the following. (Enter exact numbers as integers, fractions, or decimals.)(i)X =(ii)O =(iii)n =Part (b)In words, define the random variables X and XX is the number of tax forms that an accounting firm completes, and X is the mean number of tax forms that an accounting firm completes.X is the time needed to complete one person's tax forms, and X is the mean time needed to complete tax forms from a sample of 175 customers.X is the number of tax forms that an accounting firm completes, and X is the mean number of tax forms that an accounting firm completes.X is the time needed to complete one person's tax forms, and X is the mean time needed to complete tax forms from a sample of 175 customers.Correct! The random variable of interest, X, is the time needed to complete a person's tax form; therefore, X is the mean amount of time to complete the sample of 175 tax forms.O Part (c)Which distribution should you use for this problem? (Round your answers to two decimal places.)X- ?Explain your choice.The standard normal distribution should be used because the population standard deviation is known.The Student's t-distribution should be used because the sample standard deviation is given.The Student's t-distribution should be used because the sample mean is smaller than 30.The standard normal distribution should be used because the mean is given.Correct! To be able to use the standard normal distribution, the standard deviation of the population must be know.

Answered: Suppose that an accounting firm does a…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample mean is 23.1 hours. There is a known population standard deviation of 6.6 hours. The population distribution is assumed to be normal.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)
Find the following. (Enter exact numbers as integers, fractions, or decimals.)
(i)
X =
(ii)
O =
(iii)
n =
Part (b)
In words, define the random variables X and X
X is the number of tax forms that an accounting firm completes, and X is the mean number of tax forms that an accounting firm completes.
X is the time needed to complete one person's tax forms, and X is the mean time needed to complete tax forms from a sample of 175 customers.
X is the number of tax forms that an accounting firm completes, and X is the mean number of tax forms that an accounting firm completes.
X is the time needed to complete one person's tax forms, and X is the mean time needed to complete tax forms from a sample of 175 customers.
Correct! The random variable of interest, X, is the time needed to complete a person's tax form; therefore, X is the mean amount of time to complete the sample of 175 tax forms.
O Part (c)
Which distribution should you use for this problem? (Round your answers to two decimal places.)
X- ?
Explain your choice.
The standard normal distribution should be used because the population standard deviation is known.
The Student's t-distribution should be used because the sample standard deviation is given.
The Student's t-distribution should be used because the sample mean is smaller than 30.
The standard normal distribution should be used because the mean is given.
Correct! To be able to use the standard normal distribution, the standard deviation of the population must be know.

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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