91影视

The data is recorded for the ages of best actresses and actorsin Oscars.

A scatterplot is used to reveal the pattern of association between two variables.

Steps to sketch a scatterplot:

1. Define two axesfor the ages of actors and actresseseach year.
2. Mark each paired set of values on the graph.

The resultant scatterplot is shown below.

The correlation coefficient formula is

\(r = \frac{{n\sum {xy} - \left( {\sum x } \right)\left( {\sum y } \right)}}{{\sqrt {n\left( {\sum {{x^2}} } \right) - {{\left( {\sum x } \right)}^2}} \sqrt {n\left( {\sum {{y^2}} } \right) - {{\left( {\sum y } \right)}^2}} }}\).

For the variable of age for best actress (x) and age of best actor (y), compute the correlation coefficient.

The valuesare listedin the table below:

Substitute the values in the formula:

\(\begin{aligned} r &= \frac{{12\left( {20841} \right) - \left( {469} \right)\left( {542} \right)}}{{\sqrt {12\left( {20405} \right) - {{\left( {469} \right)}^2}} \sqrt {12\left( {25162} \right) - {{\left( {542} \right)}^2}} }}\\ &= - 0.288\end{aligned}\)

Thus, the correlation coefficient is 鈥�0.288.

Definethe actual measure of the correlation coefficient between the age of best actress and actor in Oscars as\(\rho \).

For testing the claim, form the hypotheses:

\(\begin{array}{l}{H_o}:\rho = 0\\{H_a}:\rho \ne 0\end{array}\)

The samplesize is 12 (n).

The test statistic is computed as follows:

\(\begin{aligned} t &= \frac{r}{{\sqrt {\frac{{1 - {r^2}}}{{n - 2}}} }}\\ &= \frac{{ - 0.288}}{{\sqrt {\frac{{1 - {{\left( { - 0.288} \right)}^2}}}{{12 - 2}}} }}\\ &= - 0.951\end{aligned}\)

Thus, the test statistic is鈥�0.951.

The degree of freedom is

\(\begin{aligned} df &= n - 2\\ &= 12 - 2\\ &= 10.\end{aligned}\)

The p-value is computed from the t-distribution table.

\(\begin{aligned} p{\rm{ - value}} &= 2P\left( {T < - 0.951} \right)\\ &= 0.364\end{aligned}\)

Thus, the p-value is 0.364.

Since the p-value is greater than 0.05, the null hypothes is fails to berejected.

Therefore, there is not enough evidence to conclude that there is no linear correlation between the age of actors and actresses.

It was not expected that actors and actresses have acorrelation between their ages.They can beparts of different movies.There is no clear logic for any association between their ages.