Question

A study of the effects of smoking on sleep patterns is conducted. the measure observed is the time,in minutes that it takes to fall asleep these data are obtained: smokers:69.3,56.0,22.1,47.6,53.2,48.1,52.7,34.4,60.2,43.8,23.2,13.8 Nonsmokers:28.6,25.1,26.4,34.9,29.8,28.4,38.5,30.2,30.6,31.8,41.6,21.1,36.0,37.9,13.9 (a)find the sample mean for each group (b)find the sample standard deviation for each group (c)which is more consistent data.​

Answer 1

Answer:

$\huge\tt{\bold{\purple{\underbrace{\red{\mathfrak{ɾҽզմíɾҽժ⠀αղsաҽɾ♡༄}}}}}}$

$\huge{\fbox{\pink{Given:-}}}$

Madhu spends money for $\huge{\green{Food}}$=₹850

Madhu spends money for $\huge{\blue{Petrol}}$= ₹900

$\huge{\red{Total⠀salary}}$ of Madhu = ₹12500

⠀

Prabhu spends money for $\huge{\green{Food}}$= ₹900

Prabhu spends money for $\huge{\blue{Petrol}}$= ₹950

$\huge{\red{Total⠀salary}}$ of Prabhu = ₹16500

⠀

$\huge{\fbox{\pink{Solution:-}}}$

${\purple{In ⠀Madhu's ⠀case}}$

$fraction \: of \: salary \: madhu \: spends \: on \: food \: = \frac{850}{12500} \\ \\ \implies fraction \: of \: salary \: madhu \: spends \: on \: food \: = \frac{17}{250} \\ fraction \: of \: salary \: madhu \: spends \: on \: petrol\: = \frac{900}{12500} \\ \\ \implies \: fraction \: of \: salary \: madhu \: spends \: on \: petrol\: = \frac{9}{125} \\ \\ total \: money \: madhu \: spends = 850 + 900 = 1750 \: rupees \\ \\ \implies fraction \: of \: total \: madhus \: expenditure = \frac{1750}{12500} = \frac{7}{50}$

${\purple{In⠀ Prabhu's⠀ case}}$

$fraction \: of \: salary \: prabhu \: spends \: on \: food \: = \frac{900}{16500} \\ \\ \implies fraction \: of \: salary \: prabhu \: spends \: on \: food \: = \frac{3}{55} \\ \\ fraction \: of \: salary \: prabhu \: spends \: on \: petrol\: = \frac{950}{16500} \\ \\ \implies \: fraction \: of \: salary \: prabhu \: spends \: on \: petrol\: = \frac{19}{330} \\ \\ total \: money \: prabhu \: spends = 900 + 950 = 1850 \: rupees \\ \\ \implies fraction \: of \: total \: prabhus \: expenditure = \frac{1850}{16500} = \frac{19}{330}$

⠀

Now, let us compare the fractions of theirs total expenditure to get who has more expenses.

$\frac{7}{50} \times \frac{33}{33} = \frac{231}{1650} \\ \\ \frac{37}{330} \times \frac{5}{5} = \frac{185}{1650} \\ \\ as \\ \\ \frac{231}{1650} \: is \: greater \: than \: \frac{185}{1650}$

So,

Madhu has more expenses than Prabhu.