Answered: lucose readings are 95, 86, 84, 107,…

Name: The glucose readings are 95, 86, 84, 107, 101, 112,85,86. The sample m
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Description: The glucose readings are 95, 86, 84, 107, 101, 112,85,86. The sample mean is 94.8, it is a normal distribution wirh the standard devian is 12.5, and the mean glucose is 85. Do these data indicate that Ben has an overall average level higher than 85?

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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The glucose readings are 95, 86, 84, 107, 101, 112,85,86. The sample mean is 94.8, it is a normal distribution wirh the standard devian is 12.5, and the mean glucose is 85. Do these data indicate that Ben has an overall average level higher than 85? Use a=0.05, what is the level of significance? Compute z value of the sample test statistic. Find p value

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 + ...

Expert Solution

Step 1

Total data values, i.e, glucose readings (n)= 8

The following null and alternative hypotheses need to be tested:

Ho: $\mu = 85$

Ha: $\mu > 85$

This corresponds to a right-tailed test.

The z-statistic is computed as follows:

The p-value for right tailed test and z = 2.217 is $0.0133$ , which can be found by using the standard normal table.

$Since 0 . 0133 < 0.05$ , the null hypothesis is rejected.

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