Stat 105/Sanchez
Quiz 2
x/10
ID_
NAME_
1. The angle at which electrons are emitted in muon decay has a distribution with
density
f (x | ) =
1 + x
2
1 x 1
1 1
where x =cos . The parameter is related to polarization. Physical considerations
1
dictate that
Stat 105-Practice Midterm 2
The same rules apply to this exam as in midterm 1 (closed book, closed notes; no graphic
calculators, no phones, pen or pencil). The cheat sheet can be two-sided this time, but as
before you can only have formulas and definitio
STATS 105 Homework 5 (due Wednesday 2/18/09 in class)
Exercises 9-4, 9-10, 9-14, 9-26, 9-36, 9-38, 9-52 (data online).
9-4. The mean pull-off force of a connector depends on cure time.
a. State the null and alternative hypotheses used to demonstrate that
This is a Central Limit Theorem question. We are asked to make an inference about the mean.
x is normally distribute d with 195 and 8.
For a sample of size n 25, x is normally distribute d with 195 and
8
1 .6
25
Px 193.2
z 2
n
E
2
Now find z 2 .
List the information that you are
given:
= 21
1 = .90
= .10
/2 = .05
E=3
z 2 = 1.6449
z 2
n
E
2
2
1.6449 21
132.579104 49
3
Now I lay me down to sleep, always round up when estimating sample size.
The estimated sampl
Click on this link and choose Open in StatCrunch.
You may need to use Transform data instead.
Type in this command: abs(x-mean(x) and click Compute.
Repeat the same process, only this time, overwrite the original expression with abs(y mean(y).
Click Compu
Continued.
Here is what the data looks like when it first appears in StatCrunch.
We need to sort the data with respect to gender. We do it this way.
Click on Sort Columns.
Now the data look like this.
Highlight all of the M weights in the Sort(Weight) col
Enlarge the graph and enter the data by hand into StatCrunch.
Calculate
Continued
Enter the remaining points into StatCrunch.
Next>
Calculate
For the correlation coefficient p-value, use the p-value associated with the slope.
H0: = 0 vs. HA: 0
= .05
p-va
X is normally distributed with a mean, = 167 and a standard deviation, = 26.
P(X > 159)
Continued.
X is normally distributed with a mean, = 167 and a standard error,
PX 159
n
26
15
6.7132
Continued.
Mean: = 63.6
Click Compute.
Standard Deviation: = 2.6
This is a Central Limit Theorem question. Note that the sample size, n = 48.
Mean : 63.6
Hit Compute.
Continued.
Standard Error :
n
2.6
48
.3753
State the hypotheses: H0: p = 0.6 vs. H1: p > 0.6
The alternative hypothesis indicates that this is a right tail test.
Continued on the next page.
Since were conducting a right tail
test, make sure that this inequality
points to the right.
Hit Compute.
No
I found a much easier way to do it in StatCrunch.
First click on this icon, then click on this icon and choose Open in StatCrunch.
Continued.
Heres what you should see.
Click on Graph then go to QQ Plot.
Click on QQ Plot. Heres what you should see.
In Sel
Individual mens weight are distributed normally as follows: x ~ N 178.4, 38.6
The Central Limit Theorem states that the mean weights of 42 are distributed normally as
x ~ N 178 .4, 5.9561
follows: x ~ N 178 .4, 38 .6
42
So, we want to compute this prob
np 13 .5 6.5
npq 13 .5 .5 1.80278
PAt least 6 P X 6. Applying the continuity correction we have P X 6 P X 5.5
Click on StatCrunch.
Enter the mean, the standard deviation, and make sure the inequality is pointing in the correct
direction.
Hit compute.
Co
Click on this icon then click on this icon and choose Open in StatCrunch.
Continued.
Choose var1 and make sure you check the box for Normal Quantiles on y-axis.
Hit Compute! Heres what you should see.
Continued.
n 189
p .22
q 1 p 1 .22 .78
np 189 .22 41.58
npq 189 .22 .78 5.6949
PFewer than 45 P X 45. Applying the continuity correction we have P X 45 P X 44.5
Compute
Click Next>
Continued on the next page.
Click Next>
Click Calculate
Continued on the next page.
Explained Variation
Unexplained Variation
99% Prediction Interval
2
z 2
If p is unknown, then the formula for minimum sample size is: n
.25
E
2
1.959964
n
.25 600.23
.04
Always round up to the next integer. n = 601
z 2
If p is known, then the formula for minimum sample size is: n p q
E
2
1.959964
n .99 .01
2
z 2
.25
Since p is unknown we use this equation: n
E
Confidence = 1 = .99
= .01
/2 = .005
z 2 2.575829303 (Keep all of the precision. )
E .03
2
z 2
.25
n
E
2
2.575829303
n
.25 1843 .026833
.03
Round up to the next highest integer. n = 18
Ten different categories implies n = 10. Degrees of freedom, df = n -1 = 9. = 0.10
H0: p1 = p2 = = p10 = .10
HA: At least one inequality exists.
= .10
p-value = .0532
p-value < implies that we reject the null hypothesis.
Click on that icon and choose Open in StatCrunch.
This screen should appear.
Replace all of the intervals in the Interval column with midpoints.
Continued on the next page.
Click Stat, click on Calculators, then choose Custom.
Put Interval in the Values f