We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 05 June 2012
Using the confidence interval to test a hypothesis
In the previous chapter the confidence interval was introduced as a device for estimating a population parameter. The interval can also be used to assess the plausibility of a hypothesised value for the parameter. Miller (1951) cites a study of the vocabulary of children in which the average number of words recognised by children aged 6–7 years in the USA was 24,000. Suppose that the same test had been carried out in the same year on 140 British children of the same age and that the mean size of vocabulary recognised by that sample was 24,800 with a sample standard deviation of 4,200 words. How plausible is the hypothesis that the population from which the sample of British children was chosen had the same mean vocabulary as the American children of the same age? Admittedly the sample of British children had a higher mean vocabulary size, but many samples of American children would also have had a mean score of more than 24,000. We need to rephrase the question. The mean of a sample of British children is 24,800, not 24,000. Is it nevertheless plausible that the mean vocabulary of the British population of children in this age range could be 24,000 words and that the apparent discrepancy is simply due to sampling variation, so that a new sample will have a mean vocabulary size closer to, perhaps less than, 24,000?
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
