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The correct answer for this is D. On a T-distribution we are not guaranteed
that 95% of the area will fall within 2 standard deviations of the mean, even
though this is a fact for the normal distribution.
This isn't proof for a T-distribution. Especially for when we have a small
number of observations. The answer is true, because the
researchers measured what really the entire population we can safely say that
this is a true value and there is no sample statistic involved.
The correct answer is b. the standard is a measure of variability
of the sample statistic. A is incorrect because the formula given
in a is valid only for the standard area for mean.
But we could have standard errors of a lot of other statistics as well.
For example, we could have standard errors for mo-modes and medians, and the
formula for that would not be the formula given in it.
Meanwhile, we know that the formula for the Standard Error in a mean is the
standard deviation divided by the square root of the number of observations.
In this case our standard deviation is 10.
We have 400 observations, we see that the standard data comes out to be 0.5.
The correct answer for this question is B.
The size of the smallest group, and we can illustrate that using a very simple
example. Let's say we have a case where a was 1, b
was 10, c was 100 and d was 1,000. We can see that of all expressions in the
formula come out to be one by one plus .1 plus .01 plus .001.
And we can see that the first expression is the one that are going to impact the
standard error the most. The correct answer here is d.
Different statistics have different forcumlas for standard errors.
We know that the formula for standard error of the mean.
It is given by the standard deviation divided by the square root of the number
of observations, but this is only the formula for the standard error of the
mean. We have very different formulas for the
standard errors or the mean, the modes, the median for example.
The answer to this question is d, all of the above.
The confidence interval gives us information about the effect size, the
precision and the statistical significance.
The correct answer is a, changing from a 99 to a 95% confidence level.
Because [INAUDIBLE] lower level of Confidence decreases the rate of of the
confidence interval. A 95% confidence interval of a mean will
include the true population mean 95% of the time.
This is true by the definition of the confidence interval.
If we sample both women and men together we would have a higher standard deviation
of heights because we would expect the men to be taller than the women, is the
only sample of women we would expect the heights to be closer together, because of
which the standard deviation would be lower.
The first confidence interval would be narrow, narrower because it involved a
larger sample size. We know that the formula for the margin
of error is, one by the square root of the number of observations, which comes
out to 4%. In this case, we know that the mean is
55%. In the previous question, we calculated
that when we have 625 observations, the margin of error is 4%.
So if we want to find the lower and upper bound for a 95% interval, this would be
55% plus or minus 4%. The lower bound would be 55% minus 4%,
which is 51. And the upper bound would be 55% plus 4%,
which is 59%. The correct answer is b.
Because the smallest standard error will result in a smaller p value.
The correct answer here is d. There is not enough evidence to reject
the null hypothesis. A is incorrect because we have failed to
prove that the treatments differ but this is not equivalent to proving the
treatments are the same. B is incorrect because we were not given
enough information about whether the drug in the placebo improved the insomnia
symptoms. C is incorrect because the high value, P
value shows us that we cannot reject the null hypothesis [SOUND].
In this question the correct answer is C. There is only 2% chance that the observed
difference in cure rates could have arisen if the drug had no effect.
This is by the definition of the B value.