Ch. 4 RQs
Suppose that you took one sample from a population with a mean of 13. Which of the following sample means would be MORE likely? 6,12, or both sample means are equally likely?
12
Quadrupling the sample size (i.e. 4 times N) would cut sampling error by...
50%
the 95% CI produces...
a range of plausible values for a population parameter based on expected sampling error.
As the variability in the distribution of sample means decreases, the amount of sampling error...
decreases
The probabilities produced by most research studies are...
estimates (NOT exact probabilities)
How could we make the standard error (SEM) smaller? select all that apply.
increase N, decrease σ
Researchers can decrease sampling error by _____________ the sample size.
increasing
According to the central limit theorem, the distribution of sample means...
is very often normally distributed (NOT will always have the same shape as the original popl of scores)
How is the graph of the distribution of sample means with this larger sample size (N=25) different from the distribution of sample means when the sample size was smaller (N=5)?
it is less variable (sample means are closer to the population mean; there is less sampling error)
In general, the __________ the sample, the closer the sample statistic should be to the population parameter.
larger
What shape of a distribution allows you to use the unit normal table (i.e., the z table) to determine the probabilities associated with different z scores?
normal (bell shaped)
Even if a parent/original population's distribution is skewed, the distribution of the sample means is approximately _________________ and becomes even more so as the sample size ______________.
normal, increases
Based on the results of the 95% CI you just computed you found statistical evidence that...
the greater number of orders processed by the population of experienced employees in an hour (i.e., the population parameter) might be as high as 2 more per hour or essentially 0 more per hour.
The mean of the distribution of sample means is ___________, and the standard deviation of the distribution of sample means is ______________.
the population mean; the standard error of the mean
Sampling error is the discrepancy b/w a sample statistic and a population parameter. How can you tell which samples on a graph have the most sampling error?
the samples farthest from the population (μ) have the most sampling error.
Which of the following is the best description of a distribution of sample means?
the set of means for all possible random samples of a given size (N) taken from a popl (NOT: all possible sample means taken from a popl)
The population standard deviation of σ=5 tells us that the typical distance the individual scores are away from the popl mean (μ=16) is 5. What does the standard deviation of the distribution of sample means (SEM=2.24) tell us?
the typical distance sample means are from the population means is 2.24.
T/F: According to the law of large numbers, as sample size increases, the sample mean tends to get closer to the population mean.
true
T/F: Researchers can address the problem of sampling error by using a good, nonbiased sampling procedure.
true
T/F: The Central Limit Theorem (CLT) describes the shape of the distribution of sample means for a study even if the population being investigated is skewed, as long as the sample size is sufficiently large.
true
T/F: The shape of the t distribution depends on the size of the sample.
true (as sample size increases, the t distribution becomes closer to a normal distribution and when sample sizes approach 30 the t distribution is essentially normally shaped.)
The standard error of the mean (𝑆𝐸𝑀𝑝) is the...
typical discrepancy between all possible sample means of a given size and the population mean
When computing a z for a sample mean, if the z score is far from zero, the sample mean is...
very different from the population mean and the difference is probably created by something other than sampling error.
According to the central limit theorem, the mean of the distribution of sample means will always equal what value?
μ (popl mean)
According to the central limit theorem, the standard deviation of the distribution of sample means will always equal what value?
σ/(sq. rt. of N)
Which of the following is the most accurate measure of expected sampling error in a study? 𝑆𝐸𝑀𝑝 or 𝑆𝐸𝑀𝑠
𝑆𝐸𝑀𝑝 =𝜎/√𝑁
Which of the following is NOT a true statement about 95% CIs?
BOTH A AND B CHOICES ARE TRUE: (a) values in the middle of the CI range are more plausible for the population parameter than values near the UB or LB (b) narrower CI ranges provide more accurate estimates of the population parameter than wider CI ranges
Why would we want to make the standard error smaller?
BOTH OF THE ABOVE: (1) it will reduce sampling error, and (2) the sample mean will be more likely to be close to the population mean
The typical amount of sampling error is the...
BOTH OF THE ABOVE: (1)standard deviation of the distribution of sample means, which can also be called (2) the standard error of the mean
According to the law of large numbers, the idea that larger samples represent populations more accurately, which of the following options is more likely? (Note: The mean height of women in the US is approximately 64.5 in). a) random sample of two women from US popl will have an avg height of 70 in b) random sample of 200 women from US popl will have an avg height of 70 in
a) random sample of two women from US popl will have an avg height of 70 in (smaller samples don't represent popl as well as larger ones; because average height of 70 isn't that close to the popl mean of 64.5, that mean of 70 should correspond to a smaller sample size, which in this case is 2 women)
You find the UB (upper bound) by...
adding the MOE (margin of error) to the point estimate
The shape of a distribution of sample means will...
approach a normal shape as the sample size increases.
Based on the results of the t for a sample mean you computed you concluded that drawing a sample of 100 employees with a mean number of orders processed of 35 per hour is ____________ to happen frequently based on the statistical evidence found (app. 2.41% of the time, a t score of 2 or greater when the df=99 will occur). Based on this evidence you concluded that the experienced employees probably are____________________.
not expected; are more efficient than the average employee *when you have a low p value (probability) of something occurring due to sampling error, that means that drawing that specific sample w/ that mean # of something is NOT EXPECTED (since the probability is low)*
Based on the results of the z for a sample mean you computed in this section you concluded that drawing a sample of 16 employees with a mean salary of $55,000 is ____________ to happen frequently based on the statistical evidence (probability of observed sample mean or more extreme ones was low ( . 228) so it is unlikely that these employees' higher income occurred due to chance or sampling error). Based on this evidence you concluded that the employees were probably ________________________.
not expected; doing something illegal * the probability of observed sample mean or more extreme ones was low (0.0228) so it is unlikely (NOT EXPECTED) that these employees' higher income occurred due to chance or sampling error. Perhaps the employees' salaries were higher due to illegal activities.)*
Sample statistics rarely match the population parameters they estimate exactly. The difference between the value of a sample mean (a statistic) and the population mean (a parameter) is called
sampling error
Using inferential statistics creates which of the following problems for researcher?
sampling error (NOT statistical error)
To find probabilities for the single sample t (also called t for a sample mean), you use:
statistical software
Which of the following would create a distribution of sample means?
taking all possible combinations of four ppl (i.e. all samples of four, for ex) from a population and computing each sample's mean
What is sampling error?
the difference between a sample mean and the population mean