Jen is using the large data set to investigate the relationship between Daily Maximum Relative Humidity and Daily Mean Visibility.

Using the data for Camborne, Jen takes as her sample the first

$8$

$$days of October

$2015$

$$Jen$\text{'}$s data, without units, is given in the table below.

$\backslash$

table

$[$

$[$

Daily Maximum Relative Humidity,

$93$

$,$

$92$

$,$

$97$

$,$

$98$

$,$

$100$

$,$

$99$

$,$

$91$

$,$

$96$

$]$

$,$

$[$

Daily Mean Visibility,

$1100$

$,$

$1000$

$,$

$700$

$,$

$700$

$,$

$300$

$,$

$700$

$,$

$2300$

$,$

$1600$

$]$

$]$

The Daily Mean Visibility for

$1$

$$st October was recorded as

$1100$

$($

a

$)$

$$Give an interpretation of this value, including any units.

$($

$2$

$)$

The product moment correlation coefficient for Jen's data, to

$3$

$$decimal places, is in this list

$0$

$.$

$3$

$1$

$6$

$,$

$-$

$0$

$.$

$2$

$5$

$6$

$,$

$-$

$0$

$.$

$4$

$8$

$4$

$,$

$-$

$0$

$.$

$7$

$5$

$7$

$,$

$-$

$1$

$.$

$0$

$3$

$5$

One of these values cannot be a product moment correlation coefficient.

$($

b

$)$

$$Explain which value.

$($

$1$

$)$

$($

c

$)$

$$Use your calculator to identify from the list the correct product moment correlation coefficient for Jen's data.

$($

$1$

$)$

Jen believes that the Daily Maximum Relative Humidity each day can be used to predict the Daily Mean Visibility.

$($

d

$)$

$$Carry out a suitable test, at the

$5$

$\%$

$$significance level, to show why the data may support Jen's belief.

State clearly

your hypotheses

your critical value

$($

$3$

$)$