Four different paints are advertised as having the same drying time. To check the manufacturer's claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained. Excel users: The data set is available in file named Paint. All data sets can be found on the premium online datasite. Click on the datafile logo to reference the data. (the excel data is below) Paint 1 Paint 2 Paint 3 Paint 4 128 144 133 150 137 133 143 142 135 142 137 135 124 146 136 140 141 130 131 153 At the A=0.05 level of significance, test to see whether the mean drying time is the same for each type of paint. Compute the values identified below (to 2 decimals, if necessary). Sum of Squares, Treatment Sum of Squares, Error Mean Squares, Treatment Mean Squares, Error Calculate the value of the test statistic (to 2 decimals). ___ The p-value is _ answer options (less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10) What is your conclusion? - answer options - (Conclude not all mean drying times are equal, Do not reject the assumption that the mean drying times are equalItem 7)

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Question

Four different paints are advertised as having the same drying time. To check the manufacturer's claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.

Excel users: The data set is available in file named Paint. All data sets can be found on the premium online datasite. Click on the datafile logo to reference the data. (the excel data is below)

Paint 1	Paint 2	Paint 3	Paint 4
128	144	133	150
137	133	143	142
135	142	137	135
124	146	136	140
141	130	131	153

At the A=0.05 level of significance, test to see whether the mean drying time is the same for each type of paint.

Compute the values identified below (to 2 decimals, if necessary).

Sum of Squares, Treatment
Sum of Squares, Error
Mean Squares, Treatment
Mean Squares, Error

Calculate the value of the test statistic (to 2 decimals). _________

The p-value is _______ answer options (less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10)

What is your conclusion?

- answer options - (Conclude not all mean drying times are equal, Do not reject the assumption that the mean drying times are equalItem 7)

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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