You may need to use the appropriate appendix table or technology to answer this question. According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 58 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively. (a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.) H0: Ha: (b) Using the sample from the 58 bottles, what is the test statistic? (Round your answer to three decimal places.) Using the sample from the 58 bottles, what is the p-value? (Round your answer to four decimal places.) p-value = C Repeat the preceding hypothesis test using the critical value approach. State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: Find the value of the test statistic. (Round your answer to three decimal places.) State the critical values for the rejection rule. Use ? = 0.05. (Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic≤test statistic≥

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

You may need to use the appropriate appendix table or technology to answer this question.

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 58 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.

(a)

Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.)

H₀:

H_a:

(b)

Using the sample from the 58 bottles, what is the test statistic? (Round your answer to three decimal places.)

Using the sample from the 58 bottles, what is the p-value? (Round your answer to four decimal places.)

p-value =

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

H_a:

Find the value of the test statistic. (Round your answer to three decimal places.)

State the critical values for the rejection rule. Use

? = 0.05.

(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

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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