Mathematics, 21.04.2020 17:23, frisha

A statistics lecturer poses the following question to her students as homework: 'Suppose I collected a sample and calculated the sample proportion. If I construct a 90% confidence interval for the population proportion and a 95% confidence interval for the population proportion, which of these intervals will be wider?' Three students provide their answers as follows: Tim: 'The 90% confidence interval will be wider.' Trevor: 'The 95% confidence interval will be wider.' Tracy: 'There is not enough information to tell. Either interval could be wider.'

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answered: s131845

The correct statement is provided by Trevor: 'The 95% confidence interval will be wider.'

Given that,

If construct a 90% confidence interval for the population proportion,

And a 95% confidence interval for the population proportion,

Tim: 'The 90% confidence interval will be wider.'

Trevor: 'The 95% confidence interval will be wider.

Tracy: 'There is not enough information to tell.

Either interval could be wider.'

We have to determine,

Which of these intervals will be wider.

According to the question,

Three students provide their answers as follows:

Tim: 'The 90% confidence interval will be wider.

'Trevor: 'The 95% confidence interval will be wider.

'Tracy: 'There is not enough information to tell. Either interval could be wider.'

Therefore, Confidence interval for population proportion is written as

Sample proportion ± margin of error

Margin of error $= z score \times \frac{ \sqrt{pq}}{n}$

The z score for a confidence level of 95% is higher than the z score for a confidence level of 90%.

Other things being equal, a 95% confidence level will give a higher margin of error compared to a 90% confidence level.

The higher the margin of error, the wider the confidence interval.

Therefore, The 95% confidence interval will be wider.

Hence, The correct statement is provided by Trevor: 'The 95% confidence interval will be wider.'

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answered: womankrush538

The 95% confidence interval will be wider.

Step-by-step explanation:

Confidence interval for population proportion is written as

Sample proportion ± margin of error

margin of error = z score × √pq/n

The z score is determined by the confidence level. The z score for a confidence level of 95% is higher than the z score for a confidence level of 90%

This means that with all other things being equal, a 95% confidence level will give a higher margin of error compared to a 90% confidence level.

The higher the margin of error, the wider the confidence interval. Therefore,

The 95% confidence interval will be wider.

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answered: Guest

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A statistics lecturer poses the following question to her students as homework: 'Suppose I collected...