Given sample size n = 500
Probability of bad apples in the sample =\(\frac{65}{500}\)
∴ P=0.13
∴ Probability of good apples in the sample
⇒ q = 1 - P = 1 - 0.13 = 0.87
Standard error of proportion \(=\sqrt { \frac { pq }{ n } } \)
\(=\sqrt { \frac { (0.13)(0.87) }{ 500 } } =\sqrt { \frac { 0.1131 }{ 500 } } =\sqrt { 0.000262 } \)
∴ S.E=0.015

Hypothesis testing is also referred as "Statistical Decision Making".
There are two types of statistical hypothesis
(i) Null hypothesis: which is tested for possible rejection under the assumption that it is true
(ii) Alternative hypothesis which is complementary to the null hypothesis
For example: H_o:μ=μ₀
i) H₁:μ≠μ₀ is know as two tailed alternative test
ii) H₁:μ>μ₀ and H₁:μ<μ₀ are known as one tailed alternative
iii) H₁:μ>μ₀ is said to be right tailed test where the critical region lies entirely on the right tail of the normal curve.
iv) H₁:μ<μ0 is said to the left tailed test where the critical region lies entirely on the left tail of the normal curve.

\( \text { Given } n=1000, \bar{X}=119, \sigma=30\)
\(S . E=\sigma / \sqrt{n}\)
\(=30 / \sqrt{1000} \)
\(=30 / 31.623=0.9487 \)

Errors, which arise in the normal course of investigation or enumeration on account of chance, are called sampling errors. Sampling Errors arise due to the following reasons:
a) Faulty selection of the sample instead of correct sample by defective sampling technique.
b) The investigator substitutes a convenient sample if the original sample is not available while investigation.
c) In area surveys, while dealing with border lines it depends upon the investigator whether to include them in the sample or not. This is known as Faulty demarcation of sampling units.

Here, we have to select 10 random numbers ranging from 1550 to 8000 but the given random number table has only 2 digit numbers. To solve this, two - 2 digit numbers can be combined together to make a four- figure number. Let us select the 5^th and 6^th column and combine them to form a random number, then select the random number with given range. This gives 5 random numbers, similarly, 8^th and 9^th is selected and combined to form a random numbers, then select the random number with given range. This gives 5 random numbers, totally 10 four- figure numbers have been selected. The following table shows the 10 random numbers which are combined and selected.

Therefore the selected 10 random numbers are