Question

Il Directions: Perform what is being asked Solve the problem by showing the step-by-step process.

Situation: Miko, a DOH COVID-19 tracker, found out that the number' fected persons of COVID-19 in seven

low nisk provinces of the country are 1,9, 2, 12, 8, 7, and 1 Supposed to provinces are drawn as sample,

1. What is the mean (), variance (o) and standard deation of the population (c)?

2 How many different samples of size n =6 can be drawn from the pop station?

List them with their corresponding mean

Construct the sampling distribution of the sample menn

Answer 1

Solution

1.

For a population;

mean $\mu=\dfrac{\sum X_i}{N}$

Variance $\sigma^2 =\dfrac{\sum (X_i-\mu)^2}{N}$

Standard deviation $\sigma=\sqrt\dfrac{\sum(X_i-\mu)^2}{N}$

mean $\mu = \dfrac{1+9+2+12+8+7+1}{7}$

$\mu=5.71$

Variance

$\def\arraystretch{1.5}\begin{array}{c:c:c} X_i&X_i -\mu&(X_i-\mu)^2\\\hline1&-4.71&22.18\\\hdashline1&-4.71&22.18\\\hdashline2&-3.71&13.76\\\hdashline7&1.29&1.66\\\hdashline8&2.29&5.24\\\hdashline9&3.29&10.82\\\hdashline12&6.29&39.56\\\hline \sum&&115.40\\\hline\end{array}$

$\sigma^2=\dfrac{115.4}{7}=16.49$

Standard deviation

$\sigma=\sqrt\dfrac{115.4}{7} =4.06$

2.

Population size $N=7$

Sample size $n =6$

Possible number of samples

$=C_7^6= \binom{7}{6}=7$ Samples

$\def\arraystretch{1.5}\begin{array}{c:c:c}no.& Sample & Sample mean\\\hline1&1,1,2,7,8,9&4.67\\\hdashline2&1,1,2,7,8,12&5.17\\\hdashline3&1,1,2,7,9,12&5.33\\\hdashline4&1,1,2,8,9,12&5.50\\\hdashline5&1,1,7,8,9,12&6.33\\\hdashline6&1,2,7,8,9,12&6.50\\\hdashline7&1,2,7,8,9,12&6.50\\\hline\end{array}$

Sampling distribution of the sample means

$\def\arraystretch{1.5}\begin{array}{c:c} Mean& Probability \\\hline4.67&\frac17\\\hdashline5.17&\frac17\\\hdashline5.33&\frac17\\\hdashline5.50&\frac17\\\hdashline6.33&\frac17\\\hdashline6.50&\frac27\\\hline\end{array}$