A study compared tooth health and periodontal damage in a group of 40 young adult males with a tongue piercing and a control group of 50 young adult males without tongue piercing. Here are the summary statistics:GroupSample sizeMean of enamel cracksStDev of enamel cracksTongue piercing404.13.7No Tongue piercing501.31.6 State the null and alternative hypotheses: Give the test statistic: Find the p-value: Decision and Conclusion:

Given information, Sample size of young adult males with a tongue piercing n1=40 Sample size of young adult males without a tongue piercing n2=50 Sample mean of young adult males with a tongue piercing X¯1=4.1 Sample mean of young adult males without a tongue piercing X¯2=1.3 Sample standard deviation of young adult males with a tongue piercing s1=3.7 Sample standard deviation of young adult males without a tongue piercing s2=1.6Defining the hypotheses, H0:μ1=μ2H1:μ1≠μ2 This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. The degrees of freedom will be calculated as follows: df=n1+n2-2=40+50-2=88 The critical value tc, at 0.05 significance level is ±1.987. The test statistic will be computed as follows: t=X¯1-X¯1sp1n1+1n2 where, sp=n1-1s12+n2-1s22n1+n2-2=40-1*3.72+50-1*1.6240+50-2=2.737 Solving for the test statistic, t=X¯1-X¯1sp1n1+1n2=4.1-1.32.737140+150=4.822 Since the p-value is less than 0.00001 (that is, p<0.00001), therefore, the p-value can be approximated to 0. Since the test statistic (4.822) is greater than the critical value (1.987), and the p-value (0) is less than the significance level (0.05), therefore, there is sufficient evidence to reject the null hypothesis. Hence, it can be concluded that the tooth health and periodontal damage in a group of 40 young adult males with a tongue piercing is significantly different from the tooth health and periodontal damage of a control group of 50 young adult males without tongue piercing.

Answered: A study compared tooth health and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A study compared tooth health and periodontal damage in a group of 40 young adult males with a tongue piercing and a control group of 50 young adult males without tongue piercing. Here are the summary statistics:

Group	Sample size	Mean of enamel cracks	StDev of enamel cracks
Tongue piercing	40	4.1	3.7
No Tongue piercing	50	1.3	1.6

State the null and alternative hypotheses:

Give the test statistic:

Find the p-value:

Decision and Conclusion:

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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