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Y12 - Hypothesis Testing Test

The document outlines a hypothesis testing exercise involving two scenarios: comparing the mean heights of male and female students using a t-test, and analyzing the relationship between university position and salad consumption using a chi-squared test. It includes specific tasks such as stating null and alternative hypotheses, calculating p-values, and determining whether to accept the null hypotheses based on significance levels. Additionally, it discusses a dice manufacturer's claim about the probabilities of scoring different numbers and includes calculations related to expected frequencies and goodness of fit tests.

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Siti Zaleha Maulad Abdul Hamid
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16 views6 pages

Y12 - Hypothesis Testing Test

The document outlines a hypothesis testing exercise involving two scenarios: comparing the mean heights of male and female students using a t-test, and analyzing the relationship between university position and salad consumption using a chi-squared test. It includes specific tasks such as stating null and alternative hypotheses, calculating p-values, and determining whether to accept the null hypotheses based on significance levels. Additionally, it discusses a dice manufacturer's claim about the probabilities of scoring different numbers and includes calculations related to expected frequencies and goodness of fit tests.

Uploaded by

Siti Zaleha Maulad Abdul Hamid
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Y12 - Hypothesis testing

[ 25 marks]
1. [Maximum mark: 6] SPM.1.SL.TZ0.9
Ms Calhoun measures the heights of students in her mathematics class. She is
interested to see if the mean height of male students, μ1, is the same as the
mean height of female students, μ2. 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.

(a.i) State the null hypothesis. [1]

(a.ii) State the alternative hypothesis. [1]

(b) Calculate the p-value for this test. [2]

(c) State, giving a reason, whether Ms Calhoun should accept the


null hypothesis. [2]
2. [Maximum mark: 5] SPM.1.SL.TZ0.6
As part of a study into healthy lifestyles, Jing visited Surrey Hills University. Jing
recorded a person’s position in the university and how frequently they ate a
salad. Results are shown in the table.

Jing conducted a χ2 test for independence at a 5 % level of significance.

(a) State the null hypothesis. [1]

(b) Calculate the p-value for this test. [2]

(c) State, giving a reason, whether the null hypothesis should be


accepted. [2]
. [Maximum mark: 16] EXN.2.SL.TZ0.4
3
A dice manufacturer claims that for a novelty die he produces the probability of
scoring the numbers 1 to 5 are all equal, and the probability of a 6 is two times
the probability of scoring any of the other numbers.

(a) Find the probability of scoring a six when rolling the novelty
die. [3]

(b) Find the probability of scoring more than 2 sixes when this die
is rolled 5 times. [4]

To test the manufacture’s claim one of the novelty dice is rolled 350 times and
the numbers scored on the die are shown in the table below.
(c.i) Find the expected frequency for each of the numbers if the
manufacturer’s claim is true. [
3]

A χ2 goodness of fit test is to be used with a 5% significance level.

(c.ii) Write down the null and alternative hypotheses. [2]

(c.iii) State the degrees of freedom for the test. []

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