[3] Test using independent and dependent t-test. (Show complete steps). May encode or handwritten. (Choose one t-test that is fit for the problem. Refer to the photo below)The purpose of a study by Luglie et al. was to investigate the oral status of a group of patients diagnosed with thalassemia major (TM). One of the outcome measures was the decayed, missing, and filled teeth index (DMFT). In a sample of 18 patients the mean DMFT index value was 10.3 with a standard deviation of 7.3. Is this sufficient evidence to allow us to conclude that the mean DMFT index is greater than 9.0 in a population of similar subjects? Let significance level at 0.10 INDEPENDENT / DEPENDENT T-TESTT-TEST ONE SAMPLE MEANSTEP 1: State the null and the alternative hypothesis.STEP 2: Specify the level of significance. (use a = 1% = 0.01)STEP 3: Determine the test static to be used and the degree of freedom (df).STEP 4: Compute the value of the tcomputed.tcomputed =STEP 5: Make the decision.Example:The (tcomputed = -4.00|>|tcritical = ±2.947|Since the |tcomputed| is greater than the |tcritical|, we shall reject the nullhypothesis (Ho) and accept the alternative hypothesis (Ha).STEP 6: State the conclusion.Example:At 1% level of significance with df = 15, the arithmetic mean grade of 100obtained by medical practitioners is not true.T-TEST ONE SAMPLE MEAN (GOSETT T-TEST)ž1-x2t =Ts1 (n1–1)]+[s2°(n2-1)][ni+n2] – 2[무STEP 1: State the null and the alternative hypothesis.STEP 2: Specify the level of significance.STEP 3: Determine the test static to be used and the degree of freedom (df).STEP 4: Compute the value of the tcomputed.ã1-x2t =[s1 (n1–1)]+[s2°(n2-1)][n1+n2] – 2n1STEP 5: Make the decision.STEP 6: Draw a conclusion.PAIRED T-TEST (DEPENDENT T-TEST)STEP 1: State the null and the alternative hypotheses.STEP 2: Specify the level of significance.STEP 3: Determine the test static to be used and the degree of freedom (df).STEP 4: Compute for t-static.STEP 5: Make the decision.STEP 6: Conclusion

We have given that Sample size n= 18 Sample mean = 10.3 Sample standard deviation = 7.3

Answered: The purpose of a study by Luglie et al.…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.4: Discrete Random Variables; Applications To Decision Making

Problem 9E

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[3] Test using independent and dependent t-test. (Show complete steps). May encode or handwritten. (Choose one t-test that is fit for the problem. Refer to the photo below)

The purpose of a study by Luglie et al. was to investigate the oral status of a group of patients diagnosed with thalassemia major (TM). One of the outcome measures was the decayed, missing, and filled teeth index (DMFT). In a sample of 18 patients the mean DMFT index value was 10.3 with a standard deviation of 7.3. Is this sufficient evidence to allow us to conclude that the mean DMFT index is greater than 9.0 in a population of similar subjects? Let significance level at 0.10

INDEPENDENT / DEPENDENT T-TEST
T-TEST ONE SAMPLE MEAN
STEP 1: State the null and the alternative hypothesis.
STEP 2: Specify the level of significance. (use a = 1% = 0.01)
STEP 3: Determine the test static to be used and the degree of freedom (df).
STEP 4: Compute the value of the tcomputed.
tcomputed =
STEP 5: Make the decision.
Example:
The (tcomputed = -4.00|>|tcritical = ±2.947|
Since the |tcomputed| is greater than the |tcritical|, we shall reject the null
hypothesis (Ho) and accept the alternative hypothesis (Ha).
STEP 6: State the conclusion.
Example:
At 1% level of significance with df = 15, the arithmetic mean grade of 100
obtained by medical practitioners is not true.
T-TEST ONE SAMPLE MEAN (GOSETT T-TEST)
ž1-x2
t =
Ts1 (n1–1)]+[s2°(n2-1)]
[ni+n2] – 2
[무
STEP 1: State the null and the alternative hypothesis.
STEP 2: Specify the level of significance.
STEP 3: Determine the test static to be used and the degree of freedom (df).
STEP 4: Compute the value of the tcomputed.
ã1-x2
t =
[s1 (n1–1)]+[s2°(n2-1)]
[n1+n2] – 2
n1
STEP 5: Make the decision.
STEP 6: Draw a conclusion.
PAIRED T-TEST (DEPENDENT T-TEST)
STEP 1: State the null and the alternative hypotheses.
STEP 2: Specify the level of significance.
STEP 3: Determine the test static to be used and the degree of freedom (df).
STEP 4: Compute for t-static.
STEP 5: Make the decision.
STEP 6: 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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