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Goodness of Fitness

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You own a small tea company, Sweet Leaf, NASDQ ticker symbol LEAF. You are looking at marketing costs versus benefits. Your production manager says it doesn't matter which tea you produce, all tea is the same. You say otherwise. You hire a consumer research firm headed my Matt Stat. He randomly interviews 100 consumers of your tea and the results are listed below.

BRAND PREFERRED NUMBER

Mumbo Jumbo 16
Smooth 22
Purple Passion 27
British Experience 18
China Drift 17

The competing sides are a uniform distribution like the production manager says, or what your customers say. Run a goodness of fitness test to see if the distribution is uniform, or if the brands are different.

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Solution Summary

The solution examines the goodness of fitness with statistics. Brand preferred results are analyzed.

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We use chi-squared test. The hypotheses are

H0: the distribution is uniform;

Ha: the distribution is NOT uniform.

Now we can compute the test statistic
...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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