In: Statistics and Probability
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 |
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