Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. Suppose a sample of 35 surveys produces the data in the Microsoft Excel Online file below. Use a known σ = 3.6 minutes. Is the premium rate justified?a. Formulate the null and alternative hypotheses for this application.b. Compute the value of the test statistic (to 2 decimals).c. What is the p-value (to 4 decimals)?d. Using ? = .01, is a premium rate justified for this client? Excel template - Saved ✓D46789101112131415161718192021222324252627282930313233343536373839FileHome=AInsertArialX ✓ fx13.717.314.617.418.510.115.116.61714.519.611.316.320.521.715.612.218.525.914.521.615.615.914.717.61816.711.616.81313.2BSheet1 +DrawPage Layout✓ 10сCalculation Mode: Automatic Workbook StatisticsBFormulasHypothesized Mean ValuePopulation Standard DeviationLevel of SignificanceStandard ErrorCritical ValueTest Statistic (z)p-value (Lower Tail)p-value (Upper Tail)p-value (Two Tail)Reject Null Hypothesis?Data range A:ASearch (Option + Q)DataDReviewv153.6View0.01EabHelp←GeneralF#N/A#N/A#N/A#N/A#N/A#N/A#N/A←0.00.00→.0GVHIJΣK✓Editing ✓T OvPLGive Feedback to MicrosoftMCommentsN100% + Excel template - SavedD4123456789File1011121314151617181920212223242526272829303132333425HomeACall Time (minutes)InsertArial20.313.716.218.113.717.314.617.418.510.115.116.61714.519.611.316.320.521.715.612.218.525.914.521.615.615.914.717.61816.711.616.812Sheet1B+fxDrawPage Layout10BCalculation Mode: Automatic Workbook StatisticsFormulasSample SizeSample MeanHypothesized Mean ValuePopulation Standard DeviationCDHypothesis Test about a Population Mean:Sigma Known CaseLevel of SignificanceStandard ErrorCritical ValueTest Statistic (z)p-value (Lower Tail)p-value (Upper Tail)p-value (Two Tail)Reject Null Hypothesis?&Data range A:ASearch (Option + Q)DataReview153.60.01ViewEabHelpGeneralFFormulas#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A←0.00.00→.0GHJEditingEv APVKLGive Feedback to MicrosoftMCommentsN100% +

Data 20.3 13.7 16.2 18.1 13.7 17.3 14.6 17.4 18.5 10.1 15.1 16.6 17 14.5…

Answered: Fowle Marketing Research, Inc., bases…

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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Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. Suppose a sample of 35 surveys produces the data in the Microsoft Excel Online file below. Use a known σ = 3.6 minutes. Is the premium rate justified?

a. Formulate the null and alternative hypotheses for this application.

b. Compute the value of the test statistic (to 2 decimals).

c. What is the p-value (to 4 decimals)?

d. Using ? = .01, is a premium rate justified for this client?

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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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