Video tutorial 6.1 Principles of confidence intervalsThe 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. 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. 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, *μ*_{1} - *μ*_{2}, and the difference between population proportions, *π*_{1 }- *π*_{2}. Again for the mean case, attention must be paid to whether the two population variances, *σ*^{2}_{1} and *σ*^{2}_{2} respectively, are known. If unknown, estimating the variances individually and producing a pooled estimate are considered. 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? 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. 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,

*s*^{2}, 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? 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(μ*_{X},*σ*^{2}) and $N(*μ*_{Y}, *σ*^{2}) (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 s^{2} |

*x*-data | 19 | 7.0 | 1.69 |

*y*-data | 25 | 5.1 | 2.56 |

Compute a 95% confidence interval for the difference *μ*_{X} - *μ*_{Y} between the two population means. Duration: 13 minutes 5 seconds.

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