S_x ̅ =s⁄√n is an estimate of:
the standard deviation of the sampling distribution of the mean
the standard error of the mean
o_x ̅ =o⁄√n
all of the above
The 68-95-99.7 rule indicates that for a normal distribution N(,o):
68% of the observations fall within 1 o of the mean
95% of the observations fall within 1 o of the mean
99.7% of the observations fall within 1 o of the mean
none of the above
The Law of the large numbers implies that
As the simple size increases will change being closer to x ̅
As the simple size increases the difference between the parameter and the statistic will increase
As the simple size increases the simple proportion p ̂ will be closer to the population proportion p
All of the above
When estimating the populational mean, as we increase the simple size
The simple distribution becomes more concentrated (less disperse)
The standard error decreases
The accuracy of the inference increases
Suppose we toss a fair coin 100 times. Knowing the true population of heads is 0,5 find out the 2 decimal approximation of the probability that the sample proportion of heads is between 0.4 and 0.6:
0.05
0.95
0.5
for a fixed simple size and standard error a confidence interval with a 99% confidence level is:
wider than a 95% confidence level interval
narrower than a 95% confidence level interval
of the same width than a 95% confidence level interval
wider or narrower depending on the standardized statistic (in relation to the parameter that is estimated)
the F statistic in an ANOVA used to test an average differences always increases when:
the within group variability increases
the between group variability increases
the total variability increases
We are willing to conduct a paired-samples two tailed test on the difference between the populational means of x and y. The simple mean of x is 9 and the sample mean of y is 10; the simple size is 40. The variance of the difference in sample values is s_d^2=16. What is the conclusion of our test?
We reject the null hypothesis, the populational means are significantly different
We fail to reject the null hypothesis, the populational means are not significantly different
We accept the null hypothesis, the populational means are the same
We reject the null hypothesis, the populational means are not significantly different
When the correlation coefficient between two variables x and y is larger
The estimate for the slope of the regression line has a larger value (even when the slope is negative)
The determination coefficient is also larger (even when the correlation is negative)
The determination coefficient is smaller (even when the correlation is positive)
None of the above
If we find the following confidence interval for the slope of a regression β∁ (-0.5,1.5) at a 95% confidence level:
The simple slope β ̂ is 0.5
There is no significant linear association between x and y at a 5% significance level
The simple correlation coefficient r is positive
When the determination coefficient equal 1:
There’s a perfect linear association between x and y
When y increases x increases
When y increases x decreases
Knowing that for a linear regression model Σ(
2
10
8
18
