Page 61 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing

For a two-tailed test at the significance level a, the critical regions are given as z , –z a and z . z a , whereas,
—
—
the critical region for a one-tailed test is either z , –z or z . z . 2 2
α
α
Example 9

A botanist has produced a new variety of hybrid rice grain that has better ability to resist stem borer than
other varieties. He knows that 82% of the seeds from the parent plants germinate. He claims the hybrid
has the same germination rate. 300 seeds from the hybrid plant are tested and 233 germinated. Test the
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botanist’s claim at the 2% significance level.
Solution: Let p be the proportion of seeds from the new hybrid plant germinated and p
^
be the corresponding proportion for the sample.

^
Given information: p = 0.82, n = 300, and p = 233 .
300
We are going to test whether the claim by the botanist is valid. The significance
level a is given as 0.02.

The following are the five steps in testing the hypothesis.

Step 1 : Formulate the null hypothesis and the alternative hypothesis.
H : p = 0.82
0
H : p ≠ 0.82.
1
Step 2 : Specify the significance level.

a = 0.02.

Step 3 : Select an appropriate probability distribution and determine the critical
regions.

We have
np = 300 × 0.82
= 246
5
nq = 300 × 0.18
= 54

Since both np and nq are both greater than 5, the sample size is large. We will
use the normal distribution.

This is a two-tailed test with two critical regions, one in each tail. Since the
total area of the critical regions is 0.02, the area of the critical region in each
tail is 0.01. To locate the z values, we look for 0.01 and 0.99 areas in the normal
distribution table. From the table, the z values are –2.33 and 2.33.
The critical regions: z , –2.33 and z . 2.33

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05 STPM Math(T) T3.indd 252 28/10/2021 10:24 AM