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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

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

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:

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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