Question
In: Statistics and Probability
Explain hypothesis testing to a friend, using the following scenario as a model. Describe the hypotheses,...
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 1.7 months. The P-value for the test is
0.0039. 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 less than the average recovery time for the old method
Null 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
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 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 same
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 could have a sample like this again.
It is the probability that the sample has that mean.
It is the probability that the population actually has that mean.
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 less than the 1% level that we are testing it against, allowing us to reject the null hypothesis.
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 accept the alternate 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 fail to reject the null hypothesis.
Solutions
Expert Solution
Null 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
p value: It is the probability that a sample could be gathered from the population with the given characteristics.
Type I error: Reject the hypothesis that the average recovery times are the same when in fact this is true.
type II error: Accept the hypothesis that the average recovery times are the same when in fact this is false.
That the P-value is less than the 1% level that we are testing it against, allowing us to reject the null hypothesis.
orchestra answered 2 years agoRelated Solutions
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