The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects random sample of 79 customers during a certain week, with the following results. The amount spent was X=$7.78,S=$1.62. Thirty-six customers say they "definitely will" recommend the specialty coffee shop to family and friends. Complete parts(a) through (e)At the 0.01 level of significance, is there evidence that the population mean amount was different from $6.00?Determine the Test statistics The critical values Determine the p-value State the conclusion Do no reject or reject?Is there sufficient or insufficient( select only one) evidence at the 0.01 level of significance that the population mean amount spent was different, less than, greater than or equal to( select only one) $6.00

GivenMean(x)=7.78standard deviation(s)=1.62sample size(n)=79significance level(α)=0.01claim is that the population mean amount was different from $6.00 The null and alternative hypothesis isH0:μ=6.00Ha:μ≠6.00Test statistic(t):-t=x-μsnt=7.78-6.001.6279t=9.77Test statistic is 9.77Critical value(t0):-Degrees of freedom(Df)=n-1=79-1=78α=0.01α2=0.005Critical value(t0)=±2.64 (from excel formula)P-value:-2P(t>9.77)=0.0000 (from excel formula)P-value =0.0000Conclusion:-P-value approach:-P-value is less than significance level(α)=0.01Hence Reject H0Critical value approach:-Reject H0 is test statistic is less than -2.640 or greater than +2.640Here,test statistic(t)=9.77 is greater than critical value(t0)=2.640Hence Reject H0Reject H0There is sufficient evidence at the 0.01 level of significance that the population mean amount spent was different from $6.00

Answered: The owner of a specialty coffee shop…

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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The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects random sample of 79 customers during a certain week, with the following results. The amount spent was X=$7.78,S=$1.62. Thirty-six customers say they "definitely will" recommend the specialty coffee shop to family and friends. Complete parts(a) through (e)
At the 0.01 level of significance, is there evidence that the population mean amount was different from $6.00?
Determine the Test statistics
The critical values
Determine the p-value
State the conclusion
Do no reject or reject?
Is there sufficient or insufficient( select only one) evidence at the 0.01 level of significance that the population mean amount spent was different, less than, greater than or equal to( select only one) $6.00

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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