1.1. Charlie is interested to find out if there is positive correlation between the number of letters in someone's name, $l$, and the time $t$ seconds (rounded to the nearest 5 seconds) it takes her six-year-old sister to correctly guess the spelling of the name. She looks at a random sample of names and records the results below.

Charlie carries out a one-tailed test at the 1% level of significance and finds that the critical value for this test is $0.2324$.

Find the total number of names in Charlie's sample and hence find the value of $x$.

1.2. Carry out a suitable test at the 1% level of significance to investigate whether there is positive linear correlation between the number of letters in a name and the time it takes Charlie's sister to guess the correct spelling.

You should:

• state your hypotheses clearly

• state the PMCC

1.3. Charlie calculates the equation of the regression line of $t$ on $l$ to be

$t=11.2l-33.4$

(i) Give an interpretation of the value of the gradient of this regression line.

(ii) Explain why Charlie should not use this equation to estimate the number of letters in someone's name if it took her sister 70 seconds to guess the spelling.