nd Ha: ? < 73 are to be tested using a random sample of n = 25 observations. (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) standard deviations (b) If x = 72.3, what is the conclusion using ? = 0.01? (Round your answers to two decimal places.) test statistic z = critical value z = What can you conclude? Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73.Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73.Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. (c) What is ? for the test procedure that rejects H0 when z ≤ −2.9? (Round your answer to four decimal places.) ? = (d) For the test procedure of part (c), what is ?(70)? (Round your answer to four decimal places.) ?(70) = (e) If the test procedure of part (c) is used, what n is necessary to ensure that ?(70) = 0.01? (Round your answer up to the next whole number.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with ? = 7. The hypotheses H₀: ? = 73 and H_a: ? < 73 are to be tested using a random sample of n = 25 observations.

(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.)
standard deviations

(b) If x = 72.3, what is the conclusion using ? = 0.01? (Round your answers to two decimal places.)

test statistic		z	=
critical value		z	=

What can you conclude?

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73.Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73.Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73.

z ≤ −2.9?

(Round your answer to four decimal places.)
? =

(d) For the test procedure of part (c), what is ?(70)? (Round your answer to four decimal places.)
?(70) =

(e) If the test procedure of part (c) is used, what n is necessary to ensure that ?(70) = 0.01? (Round your answer up to the next whole number.)
n = specimens

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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