Chapter 5: Statistical Data Treatment and Evaluation Flashcards
this interval defines a numerical interval around the mean of a set of replicate results within which the population mean can be expected to lie with a certain probability
confidence interval
the limits of the interval are called
confidence limits
the probability that the true mean lies
within a certain interval and is often
expressed as a percentage.
confidence level
The probability that a
result is outside the confidence interval is often called the
significance level
90% confidence interval , z=
1.64
95% confidence interval , z=
1.96
99% confidence interval , z=
2.58
formula for finding confidence interval when standard deviation population is known or s is a good estimate of the standard deviation population
CI for u=x+- z(sigma)
CI for u= mean +- z(sigma)/square root of N
TRUE or FALSE
It is essential to keep in mind at all times that confidence intervals based on CI for u= mean +- z(sigma)/square root of N apply only in the absence of bias and only if we can assume that s is a good approximation of s.
TRUE
studied the limits of the Poisson and binomial distributions,
the sampling distribution of the mean and standard deviation, and several
other topics.
W. S. Gossett
His most important work on the t test was developed to determine how closely the yeast and alcohol content of various batches of Guinness matched the standard amounts established by the brewery
W. S. Gossett
is the basis for many decisions made in science and engineering.
Hypothesis testing
postulates that two or more observed quantities are the same.
null hypothesis
Specific examples of hypothesis tests that scientists often use include the comparison
of
1) the mean of an experimental data set with what is believed to be the true
value,
2) the mean to a predicted or cutoff (threshold) value, and
3) the means or
the standard deviations from two or more sets of data.
TRUE or FALSE
The first, the null hypothesis H0, states that m population is equal to true value of mean population. The second, the alternative hypothesis Ha can be stated in several ways.
TRUE
it does not matter whether the mean is larger or smaller than the known value
two-tailed test
other alternative hypotheses are mean population > true mean population or vice versa, which indicated the direction of the difference matters and is called
one-tailed test
TRUE or FALSE
The crucial elements of a test procedure are the formation of an appropriate test statistic
and the calculation of a probability value—p-value
TRUE
TRUE or FALSE
The smaller the value of p, the stronger the evidence against H0. Conversely, if the p value is large, there is good evidence that H0 is true, and therefore, it should be accepted
TRUE
For tests concerning one or two means, the test statistic might be the ________ if we have a large number of measurements or if we know s
z statistic
used for a small number of measurements with unknown s. Also, when in doubt, it is also should be used.
t statistic
TRUE or FALSE
If the probability p of obtaining
the z (or t) value is very low when assuming H0 is true, reject H0.
TRUE
TRUE or FALSE
using the rejection region approach, if z (or t) lies within the rejection region, reject H0.
TRUE
TRUE or FALSE
The rejection region approach has fallen
out of favor because the region holds only the chosen significance level
TRUE