A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 14 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 13.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and ? is unknown. No, the x distribution is skewed left. No, the x distribution is skewed right. No, the x distribution is not symmetric.No, ? is known. How many degrees of freedom do we use? (b) What are the hypotheses? H0: ? = 13.5; H1: ? < 13.5 H0: ? < 13.5; H1: ? = 13.5 H0: ? = 13.5; H1: ? ≠ 13.5 H0: ? > 13.5; H1: ? = 13.5 H0: ? = 13.5; H1: ? > 13.5 (c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.) t = (d) Estimate the P-value for the test. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 (e) Do we reject or fail to reject H0? At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. There is sufficient evidence at the 0.05 level to reject the null hypothesis. There is insufficient evidence at the 0.05 level to reject the null hypothesis.

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Description: A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 14 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 14 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 13.5.

(a) Is it appropriate to use a Student's t distribution? Explain.

Yes, because the x distribution is mound-shaped and symmetric and ? is unknown.

No, the x distribution is skewed left.

No, the x distribution is skewed right.

No, the x distribution is not symmetric.No, ? is known.

How many degrees of freedom do we use?

(b) What are the hypotheses?

H₀: ? = 13.5; H₁: ? < 13.5

H₀: ? < 13.5; H₁: ? = 13.5

H₀: ? = 13.5; H₁: ? ≠ 13.5

H₀: ? > 13.5; H₁: ? = 13.5

H₀: ? = 13.5; H₁: ? > 13.5

t =

(d) Estimate the P-value for the test.

P-value > 0.250

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

(e) Do we reject or fail to reject H₀?

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret the results.

There is sufficient evidence at the 0.05 level to reject the null hypothesis.

There is insufficient evidence at the 0.05 level to reject the null hypothesis.

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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Solution:

Given information:

n=25 Sample size

$x = 14 S a m p l e m e a n μ = 13.5 P o p u l a t i o n m e a n s = 2 S a m p l e s \tan d a r d d e v i a t i o n α = 0.05 L e v e l o f s i g n i f i c a n c e$

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