Week 3

Question 1

what is a sampling plan?

Answer 1

a description of the approach that is used to obtain samples from a population prior to any data collection activity
- it states:
1. the objectives of the sampling activity,
2. the target population,
3. the population frame (the list from which the sample is selected),
4. the method of sampling,
5. the operational procedures for collecting the data, and
6. the statistical tools that will be used to analyze the data.

Question 2

what are subjective methods of sampling?

Answer 2

they include judgement sampling where expert judgement is used to select the sample and
- convenience sampling where samples are selected based on the ease with which data can be collected

Question 3

what is probalistic sampling?

Answer 3

involves selecting items in the sample using some random procedure, its necessary to draw valid statistical conclusions

Question 4

what is simple random sampling?

Answer 4

the most common type of probabilistic sampling approach, which involves selecting items from a population so that every subset of a given size has an equal chance of being selected

Question 5

what is systematic or periodic sampling?

Answer 5

its a sampling plan that selects every nth item from the population, eg selects member at regular interval
- its not the same as simple random sampling as for every sample, every possible sample of a given size in the population doesnt have an equal chance of being selected

Question 6

what is stratified sampling?

Answer 6

applies to populations that are divided into natural subsets (strata) and allocates the appropriate proportion of sample to each stratum

Question 7

what is cluster sampling?

Answer 7

based on dividing a population into sub groups (clusters)

Question 8

what is sampling from a continuous process?

Answer 8

selecting a sample from a continuous manufacturing process, can be done in two ways.
- First, select a time at random; then select the next n items produced after that time. this approach generally ensures that the observations will come from a homo­geneous population;
- Second, select n times at random; then select the next item produced after each of these times. However, the second approach might include items from different populations if the characteristics of the process should change over time, so caution should be used.

Question 9

what is estimation?

Answer 9

involves assessing the value of an unknown population parameter eg population mean using sample data
- estimators are the measures used to estimate population parameters

Question 10

what is a point estimate?

Answer 10

a single number derived from sample data that is used to estimate the value of a population parameter

Question 11

what is the problem with errors in point estimation?

Answer 11

One of the drawbacks of using point estimates is that they do not provide any indication of the magnitude of the potential error in the estimate.

Question 12

what is central limit theorem?

Answer 12

If the sample size is large enough, the sampling distribution of the mean is approximately normally distributed, regardless of the distribution of the population and that the mean of the sampling distribution will be the same as
that of the population.

Question 13

why do sampling statistical errors happen?

Answer 13

samples are only a subset of the total population

Question 14

what is nonsampling error?

Answer 14

occurs when the sample doesn’t represent the target population adequately.

Question 15

what is the sampling distribution of the mean?

Answer 15

the means of all possible samples of a fixed size n from some population will form a distribution -> sampling distribution of the mean

Question 16

what is an interval estimate?

Answer 16

provides a range for a population characteristic based on a sample, they provide more info than a point estimate

Question 17

what is probability interval?

Answer 17

any interval [A, B] such that the probability of falling between A and B is 1-a

Question 18

what is a confidence interval?

Answer 18

its a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true (unknown) population parameter. This probability is called the level of confidence

Question 19

what is t-distribution?

Answer 19

has a shape similar to the standard normal distribution, different t-distributions are distinguished by an degrees of freedom (df).
- The t -distribution has a larger variance than the standard normal, thus making confidence intervals wider than those obtained from the standard normal distribution, in essence correcting for the uncertainty about the true standard deviation, which is not known.

Question 20

what is a prediction interval?

Answer 20

one that provides a range for predicting the value of a new observation from the same population
-A confidence interval is associated with the sampling distribution of a statistic, but a prediction interval is associ­ated with the distribution of the random variable itself..

Question 21

what is hypothesis testing?

Answer 21

involves drawing inferences about two different propositions relating to the value of one or more population parameteres such as the mean, proportion etc

Question 22

what is null or alternative hypothesis testing?

Answer 22

The null hypothesis H0 is the hypothesis that is the default position. The alternative hypothesis H1 (sometimes denoted HA ) is the hypothesis that suggests that sample observations are influenced by a non-random cause.

Question 23

when do we reject and fail to reject the hypothesis?

Answer 23

1. reject the null hypothesis and conclude that the sample data provide sufficient statistical evidence to support the alternative hypothesis,
2. fail to reject the null hypothesis and conclude that the sample data does not support the alternative hypothesis

Question 24

how do you carry out hypothesis testing?

Answer 24

1. Identifying the population parameter of interest and formulating the hypotheses to test
2. Selecting a level of significance , which defines the risk of drawing an incorrect conclusion when the assumed hypothesis is actually true
3. Determining a decision rule on which to base a conclusion
4. Collecting data and calculating a test statistic
5. Applying the decision rule to the test statistic and drawing a conclusion

Question 25

what are the four outcomes of hypothesis testing?

Answer 25

1. The null hypothesis is actually true , and the test correctly fails to reject it .
2. The null hypothesis is actually false , and the hypothesis test correctly reaches this conclusion .
3. The null hypothesis is actually true , but the hypothesis test incorrectly rejects it (called Type I error ).
4. The null hypothesis is actually false , but the hypothesis test incorrectly fails to reject it (called Type II error ).

Question 26

what is one-tailed tests of hypothesis?

Answer 26

A one-tailed test results from an alternative hypothesis which specifies a direction. i.e. when the alternative hypothesis states that the parameter is in fact either bigger or smaller than the value specified in the null hypothesis.

Question 27

what is the p-value?

Answer 27

value means the probability, for a given statistical model that, when the null hypothesis is true, the statistical summary would be equal to or more extreme than the actual observed results

Question 28

what test do you choose when the population variance is known or not known?

Answer 28

1. Population variance is known. In Excel, choose z-Test: Two-Sample for Means from the Data Analysis menu. This test uses a test statistic that is based on the standard normal distribution.
2. Population variance is unknown and assumed unequal. From the Data Analysis menu, choose t - test: Two-Sample Assuming Unequal Variances . The test statistic for this case has a t -distribution.

Question 29

what is statistical inferences?

Answer 29

the process of drawing conclusions about an underlying population based on a sample or subset of the data
- eg One sample hypothesis testing.
Confidence Interval.
Pearson Correlation.
Bi-variate regression.
Multi-variate regression.
Chi-square statistics and contingency table.
ANOVA or T-test