# Statistics Practice Quiz Questions

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Final (Spring 2020)
Ensure that you do your own work and that you show all of your work in what you turn in
(including anything completed using R). Due at start of next class at 6:00 PM.
1. (4 points) Immediately after a ban on using hand-held cell phones while driving was
implemented, compliance with the law was measured. A random sample of 1,250 drivers
found that 98.9% were in compliance. A year after the implementation, compliance was
again measured to see if compliance was the same (or not) as previously measured. A
different random sample of 1,100 drivers found 96.9% compliance.
a) (2 Points) State an appropriate null and alternative hypothesis for testing whether or not there is
any statistical difference (i.e., a two-sided test) in these two proportions measured initially and
then one year later. Conduct the test of hypothesis using a significance level of α= 0.05. Be sure
to check the assumptions and conditions for your test. State the P-value of your test and also
state your conclusion. (Feel free to use R in showing your work - and show your commands and
output if using R.)
b) (2 points) Develop a 95% confidence interval for the true difference in proportions between the
first survey and the second survey and explain what this confidence interval means in context of
this problem. (Feel free to use R in showing your work - and show your commands and output if
using R.
Solution
Given
1250 drivers found that 98.9% were in complicance
A year later 1100 drivers found 96.9% were in complicance
a)
to find null and alternative hypothesis
We have the data given
n1 = 1250 and n2 = 1100
P1 = 0.989 and P2 = 0.969
H0 : P1 = P2
H1 : P1 = P2
α = 5% Level.

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b) By the formula
Z = P1 P2 Where P = n1* P1 + n2* P2 = 1250 * 0.989 + 1100 * 0.969 = 0.98
PQ( 1 + 1 ) n1+n2 1250 + 1100
n1 n2
So
Z = 0.989 0.969 = 3.46
0.98 * (0.02)( 1 + 1 )
1250 1100
Conclusion:
Zcd = 3.46 , Zcritical = 1.96
Zcd > Zcritical we reject H0
P value = 2 1 φ ( 0.5 + P ( 0<<<3.46)) = 0.0006
1100 (4 points) A certain golf club manufacturer advertises that its new driver (the club you use
to hit golf balls off the tee) will increase the distance that golfers achieve relative to their
current driver. We decide to test this claim by having 15 golfers hit a drive using the new
driver, and then hit one using their current driver. Here are the data for 15 people, with
yardages using both clubs:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
New
247
259
248
275
282
307
288
215
221
260
292
198
240
304
295
Current
240
254
238
268
275
301
292
197
203
262
281
189
225
297
274
a) (2 Points) Show a side-by-side boxplot of the driving distances for the current and new drivers
as well as the difference between new and current drivers (a total of three boxplots, side-by-side.
Conduct a paired t-test to test whether the new driver produces longer drives, on average, when
compared to the current driver using .05 as the probability of a Type 1 error. State your
hypotheses, and be sure to check the conditions for your test. State the P-value of your test.
(Feel free to use R in showing your work - and show your commands and output if using R.)
b) (2 points) By using a 95% confidence interval, estimate the true difference in length produced
by the new driver relative to the current one, and explain what this confidence interval means in
context of this problem. (Feel free to use R in showing your work - and show your commands
and output if using R.)

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Final (Spring 2020) Ensure that you do your own work and that you show all of your work in what you turn in (including anything completed using R). Due at start of next class at 6:00 PM. 1. (4 points) Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured. A different random sample of 1,100 drivers found 96.9% compliance. a) (2 Points) State an appropriate null and alternative hypothesis for testing whether or not there is any statistical difference (i.e., a two-sided test) in these two proportions measured initially and then one year later. Conduct the test of hypothesis using a significance level of α= 0.05. Be sure to check the assumptions and conditions for your test. State the P-value of your test and also state your conclusion. (Feel free to use R in showing your work - and show your commands and output if using R.) b) (2 points) Develop a 95% confidence interval for the true difference in proportions between the first survey and the second survey and explain what this confidence interval means in context of this problem. (Feel free to use R in showing your work - and show your commands and output if using R. Solution Given 1250 drivers found that 98.9% were in complicance A year later 1100 drivers found ...
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