State the null hypothesis, H₀, for this test.

Write down the number of degrees of freedom.

Of the 400 people Tony interviewed, 220 were male and 180 were female. 80 of the people had chosen engineering as a profession.

Calculate the expected number of female engineers.

Tony used a 5 % level of significance for his test and obtained a p-value of 0.0634 correct to 3 significant figures.

State Tony’s conclusion to the test. Give a reason for this conclusion.

Chosen profession is independent of gender.     (A1)

OR

There is no association between gender and chosen profession.     (A1)     (C1)

Note: Do not accept “not related”, “not correlated” or “not influenced”.

[1 mark]

2     (A1)    (C1)

[1 mark]

\(\frac{{180 \times 80}}{{400}}\)     (M1)

OR

\(\frac{{180}}{{400}} \times \frac{{80}}{{400}} \times 400\)     (M1)

\( = 36\)     (A1)     (C2)

[2 marks]

p-value > 0.05     (R1)

Accept H₀     (A1)     (C2)

Note: Do not award (R0)(A1).

[2 marks]

The first two parts of this question were very well answered but a number of students found calculating the required expected value in part c) difficult. Very few knew how to use the given p-value in order to decide whether to reject or retain the null hypothesis. There were some candidates who did not attempt this question at all which might be indicating that this topic had not been discussed in some schools.

The first two parts of this question were very well answered but a number of students found calculating the required expected value in part c) difficult. Very few knew how to use the given p-value in order to decide whether to reject or retain the null hypothesis. There were some candidates who did not attempt this question at all which might be indicating that this topic had not been discussed in some schools.

The first two parts of this question were very well answered but a number of students found calculating the required expected value in part c) difficult. Very few knew how to use the given p-value in order to decide whether to reject or retain the null hypothesis. There were some candidates who did not attempt this question at all which might be indicating that this topic had not been discussed in some schools.

The first two parts of this question were very well answered but a number of students found calculating the required expected value in part c) difficult. Very few knew how to use the given p-value in order to decide whether to reject or retain the null hypothesis. There were some candidates who did not attempt this question at all which might be indicating that this topic had not been discussed in some schools.