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# Statistics True or False

When testing a claim about a population proportion, the P-value method and critical value method will produce the same result when deciding whether or not to reject the null hypothesis.
A) True
B) False

In finding confidence intervals for standard deviations, the sample standard deviation if the mean of the upper and lower limit of the interval.
A) True
B) False

In finding confidence intervals for means, the sample mean is in the middle of the interval.
A) True
B) False

A Type I error is the probability of accepting a true null hypothesis.
A) True
B) False

Alpha is the same number as the probability of a Type I error.
A) True
B) False

### 1 Answer by Expert Tutors

Dattaprabhakar G. | Expert Tutor for Stat and Math at all levelsExpert Tutor for Stat and Math at all le...
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I wonder why this question remains unanswered this long.  (Probably because of ill-posed problems.)

When testing a claim about a population proportion, the P-value method and critical value method will produce the same result when deciding whether or not to reject the null hypothesis.
A) True
B) False

True.  In addition, the P-value method will also give an idea of the "extent" by which the decision is taken. For example suppose that in a particular situation, (a) the critical value corresponds to a 10% level of significance, (b) the rejection region is given by [Calculated value of the test statistic < critical value], and say, that the null hypothesis is rejected because the calculated value is smaller than the critical value.  If the P-value is 0.099, the null hypothesis will NOT be rejected at any level of significance less than 0.099.  In other words the null hypothesis is rejected only by a "marginal" extent.  In this case, due consideration should be given to how important is the choice of the level of significance to be 10 per cent.

In finding confidence intervals for standard deviations, the sample standard deviation if the mean of the upper and lower limit of the interval.
A) True
B) False

False.  (Irrelevant?  Badly worded problem?  Problem set by a person with scanty statistics background?)
A confidence interval (CI) is defined as an interval with random end-points (two statistics NOT actually computed using the available data) that contains the intended parameter of interest with a probability at least equal to a given confidence level (such as 90%).  There is no requirement that the CI for population standard deviations MUST be  based on sample standard deviations.

In finding confidence intervals for means, the sample mean is in the middle of the interval.
A) True
B) False

False (Irrelevant? etc.  See above.)  Here, there is no requirement that the CI for population mean MUST be based on sample means.

However, the statement may only appear to be true to a person with insufficient knowledge, in that s/he believes that the CI for a population mean is of the form: sample mean Y_bar plus or minus (a critical value) times either the std error of Y_bar or the the estimated std error of Y_bar, assuming a parent normal population or the conditions of the central limit theorem.

A Type I error is the probability of accepting a true null hypothesis.
A) True
B) False

False.  Type I error is an error not a probability.  Further, Type I error is the error of rejecting the null hypothesis using the data, when it is true.

Alpha is the same number as the probability of a Type I error.
A) True
B) False

False. (Badly worded problem.  What is "Alpha"?)  Even when one ASSUMES that "alpha" is the specified level of significance, the statement is false.  Alpha is a prescribed Upper Bound on the probability of Type I error.

My wish:  God save the students from such naive problem-setters!