Page 55 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing

This is a one-tailed test with a critical region at the left tail. To locate the z value,
we look for 0.01 area in the normal distribution table. From the table, the z value
is approximately –2.33.
The critical region: z , –2.33.

Step 4 : Calculate the value of the test statistic.
–
x – µ
z = σ = 3850 – 4100 = –1.838
680
n
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Step 5 : Make a decision.
To make a decision, we compare the value of the test statistic to the critical value.
This value of z = –1.838 is greater than the critical value of –2.33 and thus it
falls in the nonrejection region. We do not reject H that the average monthly
0
salary of an executive is RM4100.
Note: Example 5: Normal population and small sample, known population variance.

Example 6

The length of a particular type of iron nails produced by a manufacturer has standard deviation 6.8 mm.
The target length for an iron nail is 38 mm. A supervisor takes length measurement of a random sample
of 100 nails and obtains a sample mean length of 39.4 mm. Test whether the mean length is on target.
Use the 5% significance level.
–
Solution: Let μ be the mean length of an iron nail and x be the corresponding sample
–
mean. Given information: μ = 38 mm, s = 6.8 mm, n = 100, x = 39.4 mm.
We are going to test whether the mean length of nails meets the target length
of 38 mm. The significance level a is given as 0.05.
The following are five basic steps in testing the hypothesis.
Step 1 : State the null hypothesis and the alternative hypothesis.
H : μ = 38 mm,
0
H : μ ≠ 38 mm.
1
Step 2 : Specify the significance level.
5
a = 0.05.
Step 3 : Select an appropriate probability distribution and determine the critical
regions.
The population standard deviation s is known and the sample size is large.
–
Hence, the sampling distribution of x is approximately normal with mean µ and
standard deviation σ . We will use the normal distribution to perform the test.
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n
This is a two-tailed test with two critical regions, one at each tail. Since the total
area of the critical regions is 0.05, the area of the critical region at each tail is
0.025. To locate the z values, we look for 0.025 and 0.975 areas in the normal
distribution table. From the table, the z values are –1.96 and 1.96.
The critical regions: z , –1.96 and z . 1.96.

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05 STPM Math(T) T3.indd 246 28/10/2021 10:24 AM