Last year’s tests of gums chewed showed that the consistency would last on average for 24minutes with a standard deviation of 5.5 minutes. In a test of 36 randomly selected new gums,the gums lasted on average for 21.5 minutes. Use  of 0.01 significance level to test the claimthat the new average is different from the mean of 24 minutes. **Summary of the 9 Steps for Hypothesis Testing**1. **Null and alternative hypothesis.**2. **Two-tailed test.**3. **Select a significant level alpha.**4. **Determine T-test or Z-test.**5. **T-crit or Z-crit (Draw a graph)**6. **Calculate T-obt or Z-obt.**7. **Check whether the observed value (obt) falls in the critical region.**8. **Reject or Fail to Reject Null Hypothesis.**9. **Therefore, there is a statistically significant difference between the sample mean and the population mean OR there is no significant difference between the two means.**

Given : sample size, n = 36 sample mean, x̄ = 21.5 population standard deviation,σ=…

Answered: Last year’s tests of gums chewed showed…

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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Last year’s tests of gums chewed showed that the consistency would last on average for 24

minutes with a standard deviation of 5.5 minutes. In a test of 36 randomly selected new gums,

the gums lasted on average for 21.5 minutes. Use  of 0.01 significance level to test the claim

that the new average is different from the mean of 24 minutes.

**Summary of the 9 Steps for Hypothesis Testing**

1. **Null and alternative hypothesis.**
2. **Two-tailed test.**
3. **Select a significant level alpha.**
4. **Determine T-test or Z-test.**
5. **T-crit or Z-crit (Draw a graph)**
6. **Calculate T-obt or Z-obt.**
7. **Check whether the observed value (obt) falls in the critical region.**
8. **Reject or Fail to Reject Null Hypothesis.**
9. **Therefore, there is a statistically significant difference between the sample mean and the population mean OR there is no significant difference between the two means.**

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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