Question

In: Statistics and Probability

Russia has recently started a push for stronger smoking regulations much like those in Western countries...

Russia has recently started a push for stronger smoking regulations much like those in Western countries concerning cigarette advertising, smoking in public places, and so on. Listed below is sample data on smoking habits of Russians that are consistent with those Analyze the data and answer the following questions.

Develop a point estimate and a 95% confidence interval for the proportion of Russians who smoke.

Develop a point estimate and a 95% confidence interval for the mean annual per capita consumption (number of cigarettes) of a Russian.

For those Russians who do smoke, estimate the number of cigarettes smoked per day.

Smoker Annual Consumption Number of Cigarettes
No 0
No 0
No 0
No 0
Yes 9208
No 0
Yes 14109
Yes 7320
No 0
Yes 5738
No 0
No 0
No 0
No 0
No 0
No 0
No 0
Yes 5732
Yes 7509
No 0
No 0
Yes 18049
Yes 8109
No 0
No 0
Yes 5088
Yes 2562
No 0
No 0
No 0
Yes 7847
Yes 10633
Yes 8692
No 0
Yes 3993
No 0
No 0
No 0
Yes 2308
No 0
Yes 4136
Yes 6128
No 0
No 0
No 0
Yes 7230
No 0
No 0
No 0
Yes 5119
Yes 6213
No 0
No 0
No 0
Yes 6231
No 0
Yes 7072
Yes 7176
Yes 3016
Yes 15504
Yes 17788
Yes 8734
No 0
No 0
No 0
No 0
No 0
Yes 2281
No 0
Yes 5359
No 0
No 0
Yes 5429
No 0
Yes 2512
No 0
No 0
Yes 6295
Yes 5276
No 0
No 0
No 0
No 0
No 0
No 0
No 0
Yes 9160
Yes 8648
No 0
No 0
Yes 8661
No 0
No 0
No 0
No 0
Yes 7705
No 0
No 0
No 0
No 0
Yes 2505
Yes 7862
No 0
No 0
Yes 3973
Yes 5811
No 0
No 0
No 0
Yes 7867
No 0
Yes 8346
Yes 8756
Yes 7864
No 0
Yes 8505
No 0
No 0
No 0
No 0
No 0
Yes 5687
Yes 16767
No 0
No 0
Yes 6605
No 0
No 0
No 0
No 0
No 0
No 0
Yes 9962
No 0
No 0
No 0
Yes 8193
Yes 7513
No 0
No 0
No 0
No 0
No 0
Yes 9260
Yes 9448
No 0
Yes 7342
No 0
No 0
Yes 3657
Yes 2411
No 0
No 0
No 0
No 0
Yes 7698
No 0
Yes 2483
No 0
No 0
Yes 4547
Yes 6171
Yes 7402
Yes 7470
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
Yes 7986
Yes 6694
Yes 5072
No 0
Yes 5483
Yes 4880
No 0
No 0
No 0
No 0
Yes 6734
No 0
Yes 5086
No 0
Yes 7506
No 0
No 0
Yes 6647
Yes 6391
No 0
No 0
Yes 5879
No 0
Yes 7666
Yes 8322
Yes 8247
Yes 5127
No 0
Yes 5270
No 0
Yes 2780
Yes 7047
Yes 9456
No 0
Yes 8246
No 0
No 0
Yes 7695
No 0
No 0
No 0
No 0
Yes 6568
No 0
No 0
Yes 15853
Yes 2622
No 0
No 0
No 0
No 0
Yes 5059
Yes 8556
Yes 1825
No 0
Yes 3847
Yes 3763
Yes 6564
No 0
Yes 4620
No 0
No 0
Yes 6627
No 0
Yes 7485
Yes 5935
No 0
No 0
Yes 2895
Yes 12360
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
No 0
Yes 5962
Yes 7592
Yes 7156
No 0
No 0
No 0
No 0
No 0
Yes 5400
Yes 6989
No 0
No 0
No 0
Yes 9653
No 0
Yes 9147
No 0
Yes 5521
No 0
Yes 13651
Yes 7112
Yes 5391
No 0
No 0
No 0
No 0
Yes 8901
Yes 4902
Yes 5909
No 0
Yes 7290
No 0
No 0
No 0
Yes 8606
No 0
No 0
No 0
Yes 8716
Yes 5203
Yes 4165
Yes 6364
No 0
Yes 2702

Solutions

Expert Solution

a.
given that,
sample data on smoking habits of russians that are consistent with those analyze possibile chances (x)=134
sample size(n)=300
point of estimate = success rate ( p )= x/n = 0.4467
sample proportion = 0.4467

-------------------------------------------------------------------------------------------------------------------------------------

b.
We have considered a annual consumption number of cigarettes for smokers list within 120 members,

Annual Consumption Number of Cigarettes
count 120
mean 6,965.00
sample variance 94,35,968.22
sample standard deviation 3,071.80
minimum 1825
maximum 18049
range 16224

sample mean, x =6965
standard deviation, s =3071.8
sample size, n =120
level of significance, α = 0.05
from standard normal table, two tailed value of |t α/2| with n-1 = 119 d.f is 1.98
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 6965 ± t a/2 ( 3071.8/ Sqrt ( 120) ]
= [ 6965-(1.98 * 280.416) , 6965+(1.98 * 280.416) ]
= [ 6409.777 , 7520.223 ]

-----------------------------------------------------------------------------------------------------------------------------

c.

estimate the number of cigarettes smoked per year will be = mean rate of cigarettes per year = 6965

when considered for a single day = 6965/365 = 19.082 ~ 19 cigarettes per a day


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