Question

1. We want to test a new drug and we want to ensure that all age groups are represented it to do this we split up the general population into age groups and then select randomly within each group state what type of sampling this is and support your answer.

1b. Describe what type of distribution this is and support your answer

2. We roll 5 six-sided die. What is the probability of obtanining exactly two 1s?

3. How many license plates can we have of 3 digits followed by 3 letter? We allow repeated digital and letters.

4. What is sampling error and how would you distinguish it from non sampling error?

5. What types of inferences can we make?

6. In normal distribution what is the percentage of data having a z-score less than -1?

7. An experiment involves rolling a six sided die 480 times and recording the number of 3s. What is the mean and standard deviation?

8. What type of probability involves repeating an experiment and recording the relative frequency of the outcome?

Answer 1

1.

It is the case of cluster sampling. You make clusters of population and select randomly out of these clusters or just select random clusters. Here, it is selecting randomly out of clusters.

The distribution is normal here, as age of people follows normal distribution.

2.

When we roll a six-sided die, probability of getting any number our of 1, 2, 3, 4, 5 and 6 is (1/6).

The probability of getting a 1 in a single roll = 1/6

Probability of not getting a 1 = 5/6

Probability of getting exactly two 1s = 5C2 * (1/6 * 1/6 * 5/6 * 5/6 *5/6)

Probability of getting exactly two 1s = 10 * (125/6**5) = (10*125) / 7776 = 1250/7776 = 0.1607

We took 5C2 here as there can be many ways of selecting those 2 dice which got 1s.

3.

There are 10 digits and 26 letters.

No of ways = 10*10*10*26*26*26 = 17576000

4.

Sampling error is the error that arises in a data collection process as a result of taking a sample from a population rather than using the whole population.

Non - sampling error is the error that arises in a data collection process as a result of factors other than taking a sample. It have the potential to cause bias in polls, surveys or samples whereas sampling error doesn't have the potential to do it.