Identify The Parameter Part II For Each Of The Following Sit

Identify The Parameter Part Ii For Each Of The Following Situati

4.2 Identify the parameter, Part II. For each of the following situations, state whether the parameter of interest is a mean or a proportion.

(a) A poll shows that 64% of Americans personally worry a great deal about federal spending and the budget deficit.

(b) A survey reports that local TV news has shown a 17% increase in revenue between 2009 and 2011, while newspaper revenues decreased by 6.4% during this period.

(c) In a survey, high school and college students are asked whether or not they use geolocation services on their smartphones.

(d) In a survey, internet users are asked whether or not they purchased any Groupon coupons.

(e) In a survey, internet users are asked how many Groupon coupons they purchased over the last year.

Sample Paper For Above instruction

The determination of whether the parameter of interest in each scenario is a mean or a proportion hinges on the nature of the question being investigated. A proportion parameter pertains to the fraction or percentage of a population exhibiting a particular characteristic, while a mean parameter relates to the average value of a quantitative variable. Proper identification is critical to choosing the appropriate statistical method.

In scenario (a), the poll indicating that 64% of Americans worry about federal spending and the deficit involves a proportion. This is because the interest lies in the fraction of the population with a specific qualitative attribute—namely, concern about fiscal issues. The data are summarized as a percentage, which is a typical measure of a proportion.

Similarly, scenario (b) deals with changes in revenue figures expressed as percentages, corresponding to proportions of revenue change over time. Although these are percentage increases or decreases, the underlying data relate to the proportion of revenue change, making the parameter of interest a proportion change or difference.

In scenarios (c) and (d), the questions involve the usage of geolocation services and Groupon coupons, respectively. Both involve categorical responses—"yes" or "no"—thus making the relevant parameters proportions, representing the fraction of students or internet users engaged in these behaviors.

Contrastingly, scenario (e) pertains to the quantity of Groupon coupons purchased, which is a measurable, quantitative attribute. The interest centers on the average number of coupons bought, rendering the parameter a mean.

Identifying the correct parameter type guides analysts in selecting the suitable statistical tools, whether hypothesis testing or confidence intervals for proportions or means. An accurate classification ensures valid and meaningful inferences from the data.

References

  • Bluman, A. G. (2018). Elementary Statistics: A Step By Step Approach. McGraw-Hill Education.
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  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Routledge.

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