Download Quiz 1 – Spring `07

Section: 5____ pc#_____
508: T 12:45
509: T 2:20, 510: T 3:55
Printed Name: _______________________
UIN: ________________________
Quiz 2 plus – Fall ‘08
1. Which statement agrees with P(p40 ≥ 0.30) for p40 ∼ N(0.25, 0.0682)? n = 40
Define the following:
p40  the sample statistic, sample proportion, based on a sample of size 40
0.30  one particular value of the sample proportion
p40 ∼ N(0.25, 0.0682) (all of the parts/numbers)  the shape of the distribution of the sample proportion is normal
with mean = 0.25(center) and standard deviation = 0.068(spread).
A. What sample proportion is the upper 30% of this population with mean 0.25 and standard deviation 0.068?
The upper 30% would be an area of the Z curve, not a particular value of the sample proportion.
B. How likely are you to get 30% or more if you sample a population of 40?
Not complete information, didn’t mention mean or standard deviation.
C. How likely are you to get a probability of 0.30 if you sample a population with mean 0.25 and standard
deviation 0.068?
Again, not wrong, but still missing ‘or more’ and sample size 40.
D. How likely are you to get a sample proportion of 30% or more if you take a sample of 40 from a population with
mean 25% and standard deviation 6.8%?
Correct, all parts are mentioned.
E. Math doesn’t equate to words.
you don’t need to explain this one!
2. Let X ∼ N(7.2, 1.42). If we take a random sample of size 49 from this population, what is the distribution of the
sample mean, X 49 ?
What must be true for sample means to be at least approximately normal?
If the original data is normal, then the distribution of sample mean is exactly normal. If the original is not normal
but the sample size is sufficiently large (at least 30), then the distribution of sample mean is approximately
normal.
A. Since the sample size is large, > 30, we can say the distribution will be approximately normal with the same
mean and standard deviation.
We don’t need a large sample size since X is normal AND the standard deviation is /n NOT .
B. Since the original data is normal, we can say the distribution will be exactly normal with the same mean and
standard deviation.
The standard deviation is /n NOT .
C. Since the sample size is large, > 30, we can say the distribution will be approximately normal with the mean,
 X  7.2 and standard deviation  X  1.4 / 49 .
We don’t need the sample to be large since X is normal.
D. Since the original data is normal, we can say the distribution will be exactly normal with the mean,
and standard deviation,
 X  7.2
 X  1.4 / 49 .
Correct, shape is exactly normal, center is the same as the original and the standard deviation is /n.
2
E. X 49 ~ N (7.2, 0.029 ) .
The standard deviation is /n = 0.2.
3. What can we do to reduce the length of a 95% confidence interval for μ but leave the confidence level at 95%?
How do each of the following affect a confidence interval?
x the sample mean, is the center of the interval and doesn’t affect the width.
n is the sample size. As the sample size increases the width decreases.
 is the population standard deviation. As  increases (the data is more variable), the width increases.
 is the area outside a (1-)100%CI. As  increases, the width decreases.
z/2 is the critical value from the Z table. It is determined by the confidence level. If we want a higher confidence
level, z/2 must increase and so the width increases.
Section: 5____ pc#_____
508: T 12:45
509: T 2:20, 510: T 3:55
Printed Name: _______________________
UIN: ________________________
A. reduce the sample mean, x .
Doesn’t affect the width. It’s only the center.
B. reduce the sample size, n.
To get a narrower interval, we must INCREASE the sample size.
C. reduce the population standard deviation, .
Yes, this would reduce the width of the interval.
D. reduce the z critical value, z/2.
We want the confidence level to stay at 95%, so we cannot change the critical value.
E. Two of the above will reduce the length.
No.
4. Which of the following best describes the relationship between a (1 − )100% confidence interval for μ and a
2-sided test of hypotheses for μ = some value, μ0?
Describe the relationship between the 2-sided test of hypotheses for μ = some value, μ0 and a (1 − )100%
confidence interval for μ, both when the hypothesized value is in the interval and when it falls outside the interval
and what the p-value would be in relation to the -level. (You may then refer to this statement in your
explanations below.)
Confidence intevals provide a range of plausible values for a population parameter. If a hypothesized value, 0,
falls within a (1-)100% CI, then the value is plausible and can’t be rejected as a possible value for , so the pvalue is greater than . If a hypothesized value, 0, is outside a (1-)100% CI, then the value is NOT plausible
and will be rejected as a possible value for , so the p-value is less than .
A. There is no relationship between confidence intervals and hypothesis tests.
No, see above.
B. If the hypothesized value, μ0, falls within the confidence interval, we would reject the null.
No, we would fail to reject.
C. If the hypothesized value, μ0, falls within the confidence interval, we would fail to reject the null.
Yes, this is correct.
D. If the confidence inteval contains 0, we would reject the null.
We don’t know what the hypothesized value is but IF 0 was the hypothesized value, we would fail to reject. To
reject 0, it would have to be outside the interval.
E. If the confidence interval contains 0, we would fail to reject the null.
IF 0 was the hypothesized value, then this would be true.
5. Suppose that we want to test the hypothesis H0: μ1 =μ2 vs. HA: μ1 > μ2 with an  = 0.05. We found that the
p-value = 0.003. Which of the following statements is TRUE?
How do you determine whether to reject or not?
If p-value is less than , we reject H0. If the p-value is NOT < , we fail to reject.
What conclusion can be made when you reject?
Conclude HA is true and the test the is statistically significant.
What conclusion can be made when you fail to reject?
We canNOT conclude HA is true. We can NEVER conclude H0 is true. The test is NOT statistically significant.
A. Machine 1 has a mean significantly larger than machine 2.
Since the p-value = 0.003 <  = 0.05, we conclude HA is true, so 1, the mean of machine 1, IS larger than 2, the
mean of machine 2.
B. There is not enough evidence to reject the hypothesis that machine 1 has a larger mean than machine 2.
Yes there is since the p-value is small (less than ) we do have enough evidence. This would be the correct
conclusion if p-value >  and we failed to reject.
C. We fail to reject the hypothesis that machine 1 has smaller mean than machine 2.
We could never conclude the mean of machine 1 is smaller since that was not the alternative. We can only
conclude HA is true, never that H0 is true.
D. None of the above is TRUE.
Wrong.
E. Two of the above are TRUE.
Wrong.