Explain hypothesis testing to a friend, using the following scenario as a model. Describe the hypotheses, the sample statistic, the P-value, the meanings of Type I and Type II errors, and the level of significance. Discuss the significance of the results. Formulas are not required. A team of research doctors designed a new knee surgery technique utilizing much smaller incisions than the standard method. They believe recovery times are shorter when the new method is used. Under the old method, the average recovery time for full use of the knee is μ1 = 4.5 months. A random sample of 36 surgeries using the new method showed the average recovery time to be μ2 = 3.7 months, with sample standard deviation of 1.6 months. The P-value for the test is 0.0025. The research team states that the results are statistically significant at the 1% level of significance. Describe the hypotheses. Null hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is greater than the average recovery time for the old methodNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is less than the average recovery time for the old method Null hypothesis: the average recovery time for the new method is less than the average recovery time for the old method; Alternate hypothesis: the average recovery times are the sameNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is not the same as the average recovery time for the old method What does the P-value mean? It is the probability that a sample could be gathered from the population with the given characteristics.It is the probability that the population actually has that mean. It is the probability that the sample has that mean.It is the probability that the population could have a sample like this again. What is the meaning of a Type I error? Accept the hypothesis that the average recovery times are the same when in fact this is true.Accept the hypothesis that the average recovery times are the same when in fact this is false. Reject the hypothesis that the average recovery times are different when in fact this is true.Reject the hypothesis that the average recovery times are different when in fact this is false. What is the meaning of a Type II error? Accept the hypothesis that the average recovery times are the same when in fact this is true.Accept the hypothesis that the average recovery times are the same when in fact this is false. Reject the hypothesis that the average recovery times are different when in fact this is true.Reject the hypothesis that the average recovery times are different when in fact this is false. What does it mean to be statistically significant at the 1% level of significance? That the P-value is greater than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis.That the P-value is less than the 1% level that we are testing it against, allowing us to reject the null hypothesis. That the P-value is less than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis.That the P-value is greater than the 1% level that we are testing it against, allowing us to reject the null hypothesis.That the P-value is less than the 1% level that we are testing it against, allowing us to accept the alternate hypothesis.

Explain hypothesis testing to a friend, using the following scenario as a model. Describe the hypotheses, the sample statistic, the P-value, the meanings of Type I and Type II errors, and the level of significance. Discuss the significance of the results. Formulas are not required. A team of research doctors designed a new knee surgery technique utilizing much smaller incisions than the standard method. They believe recovery times are shorter when the new method is used. Under the old method, the average recovery time for full use of the knee is μ1 = 4.5 months. A random sample of 36 surgeries using the new method showed the average recovery time to be μ2 = 3.7 months, with sample standard deviation of 1.6 months. The P-value for the test is 0.0025. The research team states that the results are statistically significant at the 1% level of significance. Describe the hypotheses. Null hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is greater than the average recovery time for the old methodNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is less than the average recovery time for the old method Null hypothesis: the average recovery time for the new method is less than the average recovery time for the old method; Alternate hypothesis: the average recovery times are the sameNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is not the same as the average recovery time for the old method What does the P-value mean? It is the probability that a sample could be gathered from the population with the given characteristics.It is the probability that the population actually has that mean. It is the probability that the sample has that mean.It is the probability that the population could have a sample like this again. What is the meaning of a Type I error? Accept the hypothesis that the average recovery times are the same when in fact this is true.Accept the hypothesis that the average recovery times are the same when in fact this is false. Reject the hypothesis that the average recovery times are different when in fact this is true.Reject the hypothesis that the average recovery times are different when in fact this is false. What is the meaning of a Type II error? Accept the hypothesis that the average recovery times are the same when in fact this is true.Accept the hypothesis that the average recovery times are the same when in fact this is false. Reject the hypothesis that the average recovery times are different when in fact this is true.Reject the hypothesis that the average recovery times are different when in fact this is false. What does it mean to be statistically significant at the 1% level of significance? That the P-value is greater than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis.That the P-value is less than the 1% level that we are testing it against, allowing us to reject the null hypothesis. That the P-value is less than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis.That the P-value is greater than the 1% level that we are testing it against, allowing us to reject the null hypothesis.That the P-value is less than the 1% level that we are testing it against, allowing us to accept the alternate hypothesis.

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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Null hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is greater than the average recovery time for the old methodNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is less than the average recovery time for the old method Null hypothesis: the average recovery time for the new method is less than the average recovery time for the old method; Alternate hypothesis: the average recovery times are the sameNull hypothesis: the average recovery times are the same; Alternate hypothesis: the average recovery time for the new method is not the same as the average recovery time for the old method

What does the P-value mean?

It is the probability that a sample could be gathered from the population with the given characteristics.It is the probability that the population actually has that mean. It is the probability that the sample has that mean.It is the probability that the population could have a sample like this again.

What is the meaning of a Type I error?

Accept the hypothesis that the average recovery times are the same when in fact this is true.Accept the hypothesis that the average recovery times are the same when in fact this is false. Reject the hypothesis that the average recovery times are different when in fact this is true.Reject the hypothesis that the average recovery times are different when in fact this is false.

What is the meaning of a Type II error?

What does it mean to be statistically significant at the 1% level of significance?

That the P-value is greater than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis.That the P-value is less than the 1% level that we are testing it against, allowing us to reject the null hypothesis. That the P-value is less than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis.That the P-value is greater than the 1% level that we are testing it against, allowing us to reject the null hypothesis.That the P-value is less than the 1% level that we are testing it against, allowing us to accept the alternate hypothesis.

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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