Question #2A diet guide claims that you will get 120 calories in a serving of vanilla yogurt. Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving:16020022023012018014013017019080120100170Test the claim that the mean number of calories per serving of vanilla yogurt is 120. Use a significance level of 0.05.Show all the steps of your hypothesis test including The claim being tested:The null and alternative hypothesis:The test statistic

Solution-: Given: μ0=120,n=14,α=0.05 We want to find (1) The claim being tested: (2) The null and alternative hypothesis (3) The test statistic=?(1) Claim: The mean number of calories per serving of vanilla yogurt is 120(2) Hypothesis: Null hypothesis: H0:μ=μ0=120 Vs Alternative hypothesis: H1:μ≠120 This is two tailed test.(3) For test statistic: We prepare the following table: xi xi^2 160 25600 200 40000 220 48400 230 52900 120 14400 180 32400 140 19600 130 16900 170 28900 190 36100 80 6400 120 14400 100 10000 170 28900 Total 2210 374900 From this table we get, n=14 , \sum x_{i}=2210, \sum x_{i}^2=374900 Sample Mean: x¯=∑xin=221014=157.8571 and Sample variance: s2=∑xi2-n*x¯2n-1=374900-14*157.8571214-1=2002.7473 ∴s=s2=2002.7473=44.7521 Now we have, n=14,x¯=157.8571,s=44.7521 The test statistic is given by, tStat=x¯-μs/n=157.8571-12044.7521/14=3.1652

Answered: A diet guide claims that you will get…

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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Question #2

A diet guide claims that you will get 120 calories in a serving of vanilla yogurt. Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving:

160	200	220	230	120	180	140
130	170	190	80	120	100	170

Test the claim that the mean number of calories per serving of vanilla yogurt is 120. Use a significance level of 0.05.

Show all the steps of your hypothesis test including

The claim being tested:
The null and alternative hypothesis:
The test statistic

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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