A liquid soap bottle is advertised with a content of 310 milliliters (mL). Ten bottles are randomly selected and found to have contents shown below in mL. A normal probability plot indicates that you can assume the contents are normally distributed. Let μ denote the mean content of all bottles produced. To decide whether the mean content is less than advertised, perform the hypothesis test with H0:μ=310 and Ha:μ<310 at the10%significance level. Complete parts (a) through (c). 313306309299297317315296304308 a. Use the t-test. The test statistic ist=(Round to two decimal places as needed.) Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice.(Round to two decimal places as needed.) Use the Wilcoxon signed-rank test. The test statistic isW=(Round to one decimal place as needed.)Identify the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. A.The critical values are and (Type integers or decimals. Do not round. Use ascending order.) B.The critical value is(Type an integer or a decimal. Do not round.)

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Answered: A liquid soap bottle is advertised with…

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 13PPS

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A liquid soap bottle is advertised with a content of 310 milliliters (mL). Ten bottles are randomly selected and found to have contents shown below in mL. A normal probability plot indicates that you can assume the contents are normally distributed. Let μ denote the mean content of all bottles produced. To decide whether the mean content is less than advertised, perform the hypothesis test with H0:μ=310 and Ha:μ<310 at the10%significance level. Complete parts (a) through (c).

313

306

309

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297

317

315

296

304

308

a. Use the t-test.

The test statistic is

(Round to two decimal places as needed.)

Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice.

(Round to two decimal places as needed.)

Use the Wilcoxon signed-rank test.

The test statistic is

(Round to one decimal place as needed.)

Identify the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice.

The critical values are

and

(Type integers or decimals. Do not round. Use ascending order.)

The critical value is

(Type an integer or a decimal. Do not round.)

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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