stats exam 3
As N increases, what happens to size of the critical region (assume that alpha is .05)?
It does not change
upper boundary = lower boundary =
M + (tcl) (SEMs) M - (tcl) (SEMs)
the critical value for a one tailed z test with alpha = .05 is always
+1.65 and -1.65
what alpha value creates a greater probability of a type 2 error
.01
which alpha value has a lower risk of making a type 1 error
.01
what alpha value creates a greater probability of a type 1 error
.05
what alpha value results in more statistical power
.05
which alpha value has a lower risk of making a type 2 error
.05
What do you expect the numerator of the t-test to equal if the null hypothesis is true?
0
Which of the following are advantages of a using a related/repeated measures design as compared to an independent measures design? Select all that apply.
Greater statistical power with a related measures design You need fewer people in the related measures study Related measures designs control for individual differences The denominator of the t tends to be smaller for a related measures design There tends to be less sampling error for a related measures design.
two tailed research and null hypotheses for related samples t test
H1 not equal to Mu: the mean cholesterol is different than the other mean cholesterol level H0 equal to Mu: the mean cholesterol is not different than the other mean cholesterol level
two tailed research and null hypotheses for single samples t test
H1 not equal to Mu: the mean salary is not equal to other mean salary H0 equal to Mu: the mean salary is equal to other mean salary
one tailed research and null hypotheses for independent t test
H1: m1 < m2: the population of visual learners does learn better than population of verbal learners H0: m1 > or equal to m2: the population of visual learners does not learn better than population of verbal learners
two tailed research and null hypotheses for independent t test
H1: m1 is not equal to m2: would be significantly different H0: m1 = m2: wouldn't be significantly different
one tailed research and null hypotheses for related samples t test
H1<0: the mean anxiety score is lower after taking the drug than before taking it H0 > or equal to 0: the mean anxiety score is not lower after taking the drug than before taking it
one tailed research and null hypotheses for single samples t test
H1>0: mean salary is higher than other mean salary H0< or equal to 0: mean salary is not higher than other mean salary
Why was two-tailed test a more appropriate choice than a one-tailed test for the study described above?
The researcher did not have a clear prediction about which group would be more stressed
A researcher gives one group of ten people a placebo for one week and another group of 10 people an anti-anxiety drug for one week. At the end of the week she measures the anxiety levels of the people in the two groups. The researcher decides to do a one-tailed test using an alpha of .01. The anxiety levels for the placebo group M = 54.20 (SD = 8.43) were not significantly different than the anxiety levels for the drug group was M = 50.43 (SD = 9.34), t(18) = .93, p > .01, two-tailed, d =.42. How could this researcher increase statistical power in her next study? Select all that apply.
Use more people in the placebo and drug group Increase alpha to .05 Use a one-tailed test Give the drug for one month rather than one week Use a repeated measures design rather than an independent measures design
confidence intervals provide researchers with
a range of plausible values for a population parameter information that helps apply results from samples to populations
the critical value for a t test will get ________________ to 0 as sample size increases
closer
which two contribute to the width (size) of the margin of error
confidence level and expected sampling error
one tailed is otherwise known as __________________ and two tailed is otherwise known as __________________
directional, non-directional
how do you decide if you should reject the null hypothesis when using spss and doing a one tailed test
divide the sig value by 2 and then decide whether or not to reject it
to get a one tailed p value you must
divide the two tailed p value in half
True or False. Assuming everything else is held constant, as level of confidence increases, the width of the confidence interval decreases.
false
true or False. Assuming everything else is held constant, as the amount of sampling error increases, the width of the confidence interval decreases
false
the purpose of a confidence interval is to
help researchers estimate a population parameter with a specific level of confidence and precision
which common statistical assumption is not an assumption of the related samples t test
homogeneity of variance
which is not an assumption for an independent samples t test
homogeneity of variance
levene's test will help you to determine
if the two conditions have similar variances or variances that are very different (if the homogeneity of variance assumption is met or violated)
How can you decrease the denominator of the t-test?
increase N
A recent study in Sweden revealed that mothers take more sick days from work than do fathers. A different study found that men and women do not differ in the number of sick days prior to having children. What statistic could be used for both of these studies? The men and women in the studies are not couples.
indepedent samples t
Does it matter what is on the front of a box of cereal? To determine if children are influenced by the picture on the cereal box a researcher asked children to taste some cereal. All of the cereal was the same, but on half of the boxes there was a picture of a popular TV character. On the other half of the boxes there was no TV character. The children tasted the cereal and indicated how much they liked it on a scale of 1 to 5. Overall, the children who saw the popular TV character on the box thought that the cereal tasted better than the children who did not see the TV character on the box.
indepedent samples t
In the US, girls tend score lower on some types of math tests than boys. A psychologist wonders if this difference might be reflected in the toys parents request for boys and girls. The psychologist obtains records for the baby registries for 50 boys and 53 girls. For each registry he records the number of books and toys that are related to math (i.e., toys and books that involve counting, measuring, basic geometry, etc...). What statistic should be used to analyze these data?
independent samples t
Research has shown that married people tend to have better psychological health than unmarried people. A student wonders if this is true for young couples. Specifically, the student decides to obtain a sample of fifteen men who are between 19 and 20 years and are married as well as a sample of fifteen men who are between 19 and 20 years old and are single (not in a committed relationship). All men will complete a questionnaire designed to measure their psychological well-being on which scores range from 0-300 with higher numbers indicating greater psychological well-being. Which statistic should be used to analyze these data?
independent samples t
as the obtained t value increases what happens to the p value
it decreases
As N increases, what happens to the critical value (assume that alpha is .05)?
it moves closer to 0
why would a larger sample size be beneficial in this case
it would make the confidence interval more precise
In general, the higher the t-value, the _________ the p-value (assume equal df).
lower
the size of the range of plausible parameter values provided by a confidence interval is determined by the
margin of error
What is the primary advantage associated with using a one tailed test?
more statistical power
if the research hypothesis indicates that scores will decrease, the critical value will be
negative
when the obtained t value is not further from zero, then the critical value the null hypothesis should
not be rejected
one tailed significance tests have
one critical region that is either on the positive or negative side of a distribution
how to know when to use z for a sample mean
one sample mean population standard deviation is known
how to know when to use single sample t
one sample mean population standard deviation is not known (so sample standard deviation)
A market researcher wonders if consumers are influenced by the color of their orange juice. To determine if consumers prefer orange juice that is more orange, she asks shoppers to taste two "types" of orange juice. One juice is the store brand. The other juice is the store brand with food coloring added to make it appear more orange. All shoppers tasted both types of juice and rated the sweetness of each juice on a 7 point scale, with higher numbers indicating greater sweetness.
related samples t
A recent study revealed that children who were breastfed for as little as four weeks had higher grades in school than children who were not breastfed. The children in the two groups were matched on a number of important variables, including sex, birth weight, their mother's age and marital status, parents' job status and education, and their home environment.
related samples t
when you are doing a one tailed t test, the critical region Is always on the side of the t distribution that is predicted by the
research hypothesis
which of the following might be used as a point estimate in confidence intervals?
sample mean
A CEO hears that women take more sick leave after having babies and decides to work on this problem at her company. Specifically, the company institutes programs that include flexible work hours as well as the opportunity to work at home. Prior to instituting this new plan, the mean number of sick days taken by mothers in the company was µ = 10.2 per year they try to change their policies. The company plans to record the number of sick days mothers in the company take for the year following the implementation of the new program. What statistic should be used to analyze these data?
single sample t
the denominator of a t test will be __________________ if there is less sampling error
smaller
What does the number in the denominator of the t-test represent?
the expected amount of sampling error
when you locate the critical region, which distribution of sample means is the critical region on
the null distribution
What does the number in the numerator of the t-test represent?
the observed difference between means
what does the estimated standard error measure?
the typical distance between all possible sample means of a given size and the population mean
what does it mean when a researcher says that a result is statistically significant
they rejected the null hypothesis
significance/hypothesis testing helps
to asses the probability of a result being created by sampling error; if the null is rejected, it is probably not sampling error
why do researchers compute confidence intervals
to estimate a population parameter
effect size helps
to quantify a treatments effectiveness
True or False. Assuming everything else is held constant, as the sample size increases, the width of the confidence interval decreases.
true
how to know when to use repeated/related t
two sample means measure the same people twice
how to know when to use independent t
two sample means two separate groups
levene's test is automatically run by spss to determine if the ___________________ of the two groups are significantly different
variances
if p > .05 then the homogeneity of variance assumption
was not violated
when should you conduct a one tailed test
when the research hypothesis predicts scores will increase or if it predicts scores will decrease
What do you expect the numerator of the t-test to equal if the research hypothesis is true?
you can't know the exact value
A researcher wonders if children who were breastfed as babies are doing better in school because they have a higher IQ. To determine if this is the case the researcher obtains a sample of 90 children who were breastfed for at least 8 weeks as babies and measures their IQ. The mean for these children was 102 with a standard deviation of 14. Scores on a popular standardized test have a mean of 100 with a standard deviation of 15. Is there evidence that the children who were breastfed have a higher IQ than the general population?
z for a sample mean
