Assume that a simple random sample has been selected and test the given claim. Use the P-value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. The ages of actresses when they won an acting award is summarized by the statistics n=78, x=35.1 years, and s=11.4 years. Use a 0.01 significance level to test the claim that the mean age of actresses when they win an acting award is 33 years. Question content area bottom Part 1 What are the hypotheses? A. H0: μ=33 years H1: μ≥33 years B. H0: μ=33 years H1: μ≠33 years C. H0: μ≠33 years H1: μ=33 years D. H0: μ=33 years H1: μ<33 years Part 2 Identify the test statistic. t=enter your response here (Round to three decimal places as needed.) Part 3 Identify the P-value. The P-value is enter your response here. (Round to four decimal places as needed.) Part 4 State the final conclusion that addresses the original claim. Choose the correct answer below. A. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years. B. Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years. C. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years. D. Reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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Assume that a simple random sample has been selected and test the given claim. Use the P-value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
The ages of actresses when they won an acting award is summarized by the statistics n=78, x=35.1 years, and s=11.4 years. Use a 0.01 significance level to test the claim that the mean age of actresses when they win an acting award is 33 years.
Question content area bottom
Part 1
What are the hypotheses?
A.
H0: μ=33 years
H1: μ≥33 years
B.
H0: μ=33 years
H1: μ≠33 years
C.
H0: μ≠33 years
H1: μ=33 years
D.
H0: μ=33 years
H1: μ<33 years
Part 2
Identify the test statistic.
t=enter your response here (Round to three decimal places as needed.)
Part 3
Identify the P-value.
The P-value is enter your response here. (Round to four decimal places as needed.)
Part 4
State the final conclusion that addresses the original claim. Choose the correct answer below.
A.
Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.
B.
Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.
C.
Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.
D.
Reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

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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