block 5-8 Flashcards
(39 cards)
fill in the blanks:
if sample is large enough, the distribution of sample means ____(will/ won’t) be normal, even though the distribution of data in pop _____ (is/ isn’t) normal
if sample is large enough, the distribution of sample means will be normal, even though the distribution of data in pop is NOT normal
The mean of what, is the true population mean?
The mean of the sampling distribution of means is the true population mean
fill in the blanks:
Since the sample distribution is normal: ___% of the sample mean falls within ____ times the standard error.
Since the sample distribution is normal: 95% of the sample mean falls within 1.96 times the standard error.
What is the sampling distribution of a mean?
The sampling distribution of a mean = the distribution of sample means.
What is confidence interval?
Interval around the estimated mean where we have a certain level of confidence that it contains the true mean.
Does the confidence interval tell us the probability that an interval contains the true mean?
No, it does not tell us the probability that the confidence interval contains the true mean, because true mean is a fixed point and it either is or is not in the interval.
Fill in the blank:
The confidence interval extends to _____ side of the mean by a multiple of _______.
Most commonly is calculated to be what ___
The confidence interval extends to either side of the mean by a multiple of the standard error.
Mostly commonly calculated as 95% CI, this extends 1.96 SE either side of the mean.
Fill in the blank:
If we took thousands of samples, and for each sample calculated the mean and associated 95% confidence interval, we would expect ___% of these confidence intervals to include the population mean.
If we took thousands of samples, and for each sample calculated the mean and associated 95% confidence interval, we would expect 95% of these confidence intervals to include the population mean.
What is the formula for calculating the confidence interval?
What information is necessary?
95% confidence interval = x ± 1.96 SE (x)
(the x’s have lines above them)
x = mean height
SE (x) = standard error
What multiple is used when calculating a:
90% CI
95% CI
99% CI
90% CI – 1.56
95% CI – 1.96
99% CI – 2.56
what is the z value, and what is its formula
z value = test statistic
formula
(estimated mean - hypothesized mean)/ SE
(pg 29, BS05)
If the “Distribution of x if Null Hypothesis were true”, was plotted as a normal distribution, which part of the distribution curve corresponds with the p value?
Again, what is the z value?
Z value is the test statistic, to calculate the difference between the estimated mean and the hypothesized mean.
The P value is area under the curve that’s distal to the z values.
What does a large p-value mean?
If the p-value is large, the chance of observing the value as extreme as the sampled one is high if the Null Hypothesis were true.
-or-
The larger the p-value, the less evidence against Null Hypothesis (no difference).
A small p value means?
The chance of observing this value if the Null Hypothesis were true, is low. More evidence against Null. That the value is less likely due to sample variation and more likely to reflect a real difference.
If the hypothesized mean is NOT included in the 95% CI, this is evidence FOR or AGAINST the null hypothesis?
If hypothesized mean is NOT included in the 95% CI, this is evidence against the Null Hypothesis, meaning there is likely a real difference.
fill in the blanks
When the sample size is small, ______ is not a good approximation, rather ______ is used.
When the sample size is small, normal distribution is not a good approximation, rather t-distribution is used.
What determines the shape of a t-distribution?
Degrees of freedom.
What are degrees of freedom?
Degrees of freedom are a measure of how small the sample size is. It determines the shape of the t-distribution curve.
t distribution = sample size minus 1
The smaller the degrees of freedom mean what?
Smaller degrees of freedom mean lower the probabilities around the mean and higher the probabilities at the tails. The curve is shorter and wider.
How does increasing degrees of freedom affect the t-distribution curve in relation to the normal distribution curve?
Bigger degrees of freedom mean larger sample sizes, which means the t-distribution resembles the normal distribution curve more and more.
What is the formula for the 95% CI of mean for small sample size?
estimated mean +/- multiplier x standard error of estimate
multiplier = value of t corresponding to a two sided p = 0.05
In what situations are two tailed and one tailed used for p-values?
Most commonly, 2 tailed used because the alternative hypothesis simply states the estimated mean is not equal to the hypothesized mean.
H1: u ≠ u0
Less commonly, 1 tailed is used when alternative hypothesis is:
H1: u > u0. or u < u0
Historically, what p value is deemed “enough” evidence
p < 0.05
Fill in the blank:
When the result of a test has a P-value smaller than 0.05, the 95% confidence interval _____ (will/ won’t) include the hypothesized value.
When the result of a test has a P-value smaller than 0.05, the 95% confidence interval will not include the hypothesized value.
