SPM.1.SL.TZ0.9

pestleMathematicsAISLPaper 1SPM· sl-4-11-expected-observed-hypotheses-chi-squared-gof-t-testsource ↗

Ms Calhoun measures the heights of students in her mathematics class. She is interested to see if the mean height of male students, ${\mu _1}$ , is the same as the mean height of female students, ${\mu _2}$ . The information is recorded in the table.

At the 10 % level of significance, a $t$ -test was used to compare the means of the two groups. The data is assumed to be normally distributed and the standard deviations are equal between the two groups.

State the null hypothesis.

[1]

a.i.

State the alternative hypothesis.

[1]

a.ii.

Calculate the $p$ -value for this test.

[2]

State, giving a reason, whether Ms Calhoun should accept the null hypothesis.

[2]

Markscheme / solution

${\mu _1} - {\mu _2} = 0$ A1

Note: Accept equivalent statements in words.

[1 mark]

a.i.

${\mu _1} - {\mu _2} \ne 0$ A1

Note: Accept equivalent statements in words.

[1 mark]

a.ii.

0.296 (0.295739…) A2

[2 marks]

0.296 > 0.1 R1

fail to reject the null hypothesis, there is no difference between the mean height of male and female students A1

Note: Award (R1) for a correct comparison of their $p$ -value to the test level, award (A1) for the correct interpretation from that comparison.
Do not award R0A1.

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]