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Coin Operated Drink Machine Hypothesis Testing

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Problem

A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 12 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.85 ounces and 0.23 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, mu, differs from 7 ounces?
Perform a two-tailed test. Then fill in the table below.

Problem:

Null hypothesis: H0:______

Alternative hypothesis: H1:______

Type of test statistic: (Z, t, Chi squared, F)

Value of test statistic:______

The two critical values at the 0.1 level of significance:____, ____

At the 0.1 level of significance, can we conclude that the true mean discharge differs from 7 ounces?: (Yes/No)

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Solution Summary

The solution tests hypotheses for a coin operated drink machine and its discharge.

Solution Preview

A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 12 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.85 ounces and 0.23 ...

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  • 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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