A random sample of 36 pizzas at Vinnie Gumba's Pizza Joint yields the following results for their 12 Inch Pizza:the sample mean diameter of pizzas equals 11.5 inches14 people out of 36 ordered the “Gumba Special”, pizza (pineapple, anchovies, and garlic)it is known from previous studies that the sample standard deviation equals 2.0 inches.1. What sample size is required if you want to be 90% sure that the sample mean will be within 0.1 inches of the true mean?2. Test the hypothesis that the true population mean of a small pizza is less than 12 inches. Set the Type I error equal to 1%.3. Test the hypothesis that the true population means of a small pizza is not equal to 12 inches. Set the Type I error equal to 10%.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A random sample of 36 pizzas at Vinnie Gumba's Pizza Joint yields the following results for their 12 Inch Pizza:

the sample mean diameter of pizzas equals 11.5 inches
14 people out of 36 ordered the “Gumba Special”, pizza (pineapple, anchovies, and garlic)
it is known from previous studies that the sample standard deviation equals 2.0 inches.

1. What sample size is required if you want to be 90% sure that the sample mean will be within 0.1 inches of the true mean?

2. Test the hypothesis that the true population mean of a small pizza is less than 12 inches. Set the Type I error equal to 1%.

3. Test the hypothesis that the true population means of a small pizza is not equal to 12 inches. Set the Type I error equal to 10%.

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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