While reading a published research report, the following is reported: “When we examined the critical skills data, the mean of 50.00 from the sample of 200 adolescents differed significantly from the population mean of 53.5, [t(199) = 3.54, p<.05].” For letters a-h, identify all that’s given. Indicate "not known" or “not given” where applicable. ### Statistical Analysis GuideThis section covers the key statistical symbols and questions involved in a hypothesis testing scenario.#### Variables and Symbols:- **a. μ =** Population mean.- **b. σ =** Population standard deviation.- **c. X bar =** Sample mean.- **d. sx =** Sample standard deviation.- **e. N =** Sample size.- **f. α =** Significance level, typically set at 0.05 or 0.01 for hypothesis testing.- **g. tobt =** Obtained t-value from the t-test.- **h. tcrit =** Critical t-value from the t-distribution table.#### Hypothesis Testing Questions:- **i.** Does the sample of adolescents differ significantly from the population mean? Support your answer by comparing the obtained t-value (tobt) to the critical t-value (tcrit). If tobt is greater than tcrit, the sample mean is significantly different from the population mean.- **j.** Is there a significant difference between the two means at an alpha level of 0.01? Explain your answer by assessing whether the p-value is less than 0.01, indicating statistical significance at the 1% level. If the obtained t-value exceeds the critical t-value at this significance level, the difference is significant. 3. While reading a published research report, the following is reported: “When we examined the critical skills data, the mean of 50.00 from the sample of 200 adolescents differed significantly from the population mean of 53.5, [t(199) = 3.54, p < .05].”For letters a-h, identify all that’s given. Indicate "not known" or “not given” where applicable.

Answered: Image /qna-images/answer/278953fe-0288-4437-b47c-81c006666495.jpg i. The sample meah differs significantly from the populatibn mean. This is because it is given that the p-value is less than 0.05. And we know that when the p-value is less than the level of significance here 0.05 we reject null hypothesis(which states that the sample mean do not differ from the population mean) and conclude that there is a significant difference. j. When the level of significance is 0.01, we cannot make any conclusions since in the question it is not mentioned whether the p value is less than 0.01 also.If however we assume that the p value is less than 0.05 but not less than 0.01, then we may accept that there is no significant difference between the sample mean and population mean.

Answered: While reading a published research…

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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While reading a published research report, the following is reported: “When we examined the critical skills data, the mean of 50.00 from the sample of 200 adolescents differed significantly from the population mean of 53.5, [t(199) = 3.54, p<.05].”

For letters a-h, identify all that’s given. Indicate "not known" or “not given” where applicable.

### Statistical Analysis Guide

This section covers the key statistical symbols and questions involved in a hypothesis testing scenario.

#### Variables and Symbols:

- **a. μ =** Population mean.
- **b. σ =** Population standard deviation.
- **c. X bar =** Sample mean.
- **d. sx =** Sample standard deviation.
- **e. N =** Sample size.
- **f. α =** Significance level, typically set at 0.05 or 0.01 for hypothesis testing.
- **g. tobt =** Obtained t-value from the t-test.
- **h. tcrit =** Critical t-value from the t-distribution table.

#### Hypothesis Testing Questions:

- **i.** Does the sample of adolescents differ significantly from the population mean? Support your answer by comparing the obtained t-value (tobt) to the critical t-value (tcrit). If tobt is greater than tcrit, the sample mean is significantly different from the population mean.

- **j.** Is there a significant difference between the two means at an alpha level of 0.01? Explain your answer by assessing whether the p-value is less than 0.01, indicating statistical significance at the 1% level. If the obtained t-value exceeds the critical t-value at this significance level, the difference is significant.

3. While reading a published research report, the following is reported: “When we examined the critical skills data, the mean of 50.00 from the sample of 200 adolescents differed significantly from the population mean of 53.5, [t(199) = 3.54, p < .05].”

For letters a-h, identify all that’s given. Indicate "not known" or “not given” where applicable.

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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