A sample of 213 newspaper tire ads from several Sunday...

Name: Problem 77, Chapter 8: Applied Statistics in Business and Economics
Uploaded: 2021-02-02T15:24:04-08:00
Duration: 1 min 31 s
Channel: Hossam Mohamed
Description: A sample of 213 newspaper tire ads from several Sunday papers showed that 98 contained a lowprice guarantee (offer to "meet or beat any price"). (a) Assuming that this was a random sample, construct a 95 percent confidence interval for the proportion of all Sunday newspaper tire ads that contain a low-price guarantee. (b) Is the criterion for normality met?

A sample of 213 newspaper tire ads from several Sunday papers showed that 98 contained a lowprice guarantee (offer to "meet or beat any price"). (a) Assuming that this was a random sample, construct a 95 percent confidence interval for the proportion of all Sunday newspaper tire ads that contain a low-price guarantee. (b) Is the criterion for normality met?

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Key Concepts

Confidence Interval for a Proportion

This concept involves estimating the true proportion of a population that exhibits a certain characteristic based on a sample. By calculating the sample's proportion and then adding and subtracting a margin of error (computed using the standard error and a critical value from the normal distribution), one obtains an interval that likely contains the population proportion with a specified degree of confidence (e.g., 95%).

Standard Error for a Proportion

The standard error measures the variability of the sample proportion and is calculated using the formula ?[p?(1 - p?)/n], where p? is the sample proportion and n is the sample size. This metric is crucial in quantifying the precision of the sample estimate and plays a key role in determining the margin of error used in confidence intervals.

Normal Approximation and the Central Limit Theorem

For large enough sample sizes, the sampling distribution of the proportion can be approximated by a normal distribution, according to the central limit theorem. A commonly used rule is that both np? and n(1 - p?) should be at least 10. This normality criterion ensures that the confidence interval constructed using the normal distribution is valid.

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