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Monday, March 23, 2009
STATISTICS Madness Video tutorial 6.1 Principles of confidence intervals The key ingredients to confidence intervals are outlined as well as their interpretation as a indicator to the level of uncertainty attached to a point estimate. A generic template is offered which can subsequently be applied to the various scenarios encountered in Statistics 1. To view the video, click here. Duration: 11 minutes 50 seconds. Video tutorial 6.2 Review of confidence interval scenarios: single parameters Building on the generic template given in Video tutorial 6.1, the different scenarios of single point estimates which appear in the Statistics 1 subject guide are reviewed. These comprise confidence intervals estimating a single population mean, μ, and a single population proportion, π. For the former case involving means, consideration must be given to whether the population variance, σ 2, can be assumed to be known and, if not, the mechanism for dealing with this is discussed. To view the video, click here. Duration: 15 minutes 26 seconds. Video tutorial 6.3 Review of confidence interval scenarios: differences between two parameters This Video tutorial extends Recording 6.2 to consider constructing confidence intervals for differences between two population means, μ1 - μ2, and the difference between population proportions, π1 - π2. Again for the mean case, attention must be paid to whether the two population variances, σ21 and σ22 respectively, are known. If unknown, estimating the variances individually and producing a pooled estimate are considered. To view the video, click here. Duration: 19 minutes 27 seconds. Video tutorial 6.4 Computing minimum sample size to achieve a given confidence interval width Question: James thought the population proportion of the electorate who intended to vote for the incumbent government in the forthcoming election was 34%. To investigate this hunch he decides to estimate this with a sample proportion. He sets a tolerance limit of 0.10 with 90% confidence. What is the minimum sample size required? To view the video, click here. Duration: 11 minutes 12 seconds. Video tutorial 6.5 Confidence interval for the difference in proportions Question: A researcher was investigating computer usage among students at a particular university. 200 undergraduates and 100 postgraduates were chosen at random and asked if they owned a laptop. It was found that 81 of the undergraduates and 63 of the postgraduates did. Find a 95% confidence interval for the difference in the proportion of undergraduates and postgraduates who own a laptop. To view the video, click here. Duration: 9 minutes 34 seconds. Video tutorial 6.6 Confidence interval for a population mean, variance unknown Question: A random sample of 8 students was taken and their scores in a statistics paper recorded. The sample mean was calculated to be = 71.2$ and the sample variance, s2, was 4.9. Compute a 99% confidence interval for the mean statistics score for all students taking the course. How can the interval width be made narrower? Why? To view the video, click here. Duration: 11 minutes 34 seconds. Video tutorial 6.7 Confidence interval for the difference in population means, variances unknown Random samples are taken from two populations with distribution N(μX,σ2) and $N(μY, σ2) (i.e. their variances are the same). The summary statistics for the two samples are as follows: Sample size, n Sample mean, m Sample Variance s2 x-data 19 7.0 1.69 y-data 25 5.1 2.56 Compute a 95% confidence interval for the difference μX - μY between the two population means. To view the video, click here. Duration: 13 minutes 5 seconds. Video tutorial 7.1 Principles of hypothesis testing Similar to Recording 6.1 for confidence intervals, this video explains the mechanics of hypothesis testing. Formation of the hypotheses is discussed along with the concept of a test statistic and its associated distribution. Specification of a significance level, α, is covered and its role in determining critical values in order to define an appropriate critical/rejection region. Interpretation of how to draw conclusions from comparing an observed test statistic value with the critical values is also covered. To view the video, click here. Duration: 40 minutes 47 seconds. Video tutorial 7.2 Test statistic scenarios This recording is the hypothesis testing equivalent of Recordings 6.2 and 6.3. All the test statistics associated with testing (i) single population means (ii) differences between population means (iii) single population proportions and (iv) differences between population proportions are covered. Just as with confidence intervals, unknown population variances must be treated appropriately when testing means. To view the video, click here. Duration: 23 minutes 23 seconds. Video tutorial 7.3 Testing a single population mean Question: It may be assumed that the length of nails produced by a particular machine is a normally distributed random variable, with standard deviation 0.02 cm. The lengths of a sample of 5 nails are 1.14, 1.15, 1.14, 1.12 and 1.16 cm. Test, at the 5% significance level, the hypothesis that the machine produces nails with a mean length 1.12 cm. To view the video, click here. Duration: 9 minutes 51 seconds. Video tutorial 7.4 Testing the difference between population means Question: The mean reaction times, in hundredths of a second, of two groups of subjects to a flashing-light stimulus are measured. The first group, denoted by subscript 1, comprised individuals who were new to the experiment while the subjects in the second group, denoted by subscript 2, had previously taken part. Summary statistics for the two samples are given below. 1 = 3.0 s21 = 0.064 n1 = 10 2 = 2.7 s22 = 0.031 n2 = 8 Test if experience has had an effect on the mean response time. To view the video, click here. Duration: 15 minutes 25 seconds. Video tutorial 7.5 Testing a single population proportion Question: An accounting firm wishes to test the claim that no more than 1% of a large number of transactions contains errors. In order to test this claim, they examine a random sample of 144 transactions and find that exactly 3 of these are in error. What conclusion should the firm draw? To view the video, click here. Duration: 11 minutes 0 seconds. Video tutorial 7.6 Testing the difference between population proportions Question: A market research company has conducted a survey of adults in two large towns, either side of an international border, in order to judge attitudes towards a controversial internationally broadcast celebrity television programme. The following table shows some of the information obtained by the survey: Town A Town B Sample size 40 40 Sample number approving of the programme 24 22 Conduct a formal hypothesis test, at the 5% significance level, of the claim that the population proportions approving the programme in the two towns are equal. To view the video, click here. Duration: 12 minutes 11 seconds. Half way through, my mind seems to be blank. ENDURE for this 2 months!! Jia you x 1000000! |
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