Question

Many groups are interested to know if the proportion of Idaho residents who smoke is different than 18% (which was the national proportion of adults who smoke in 2014 according to the CDC). A random sample of Idahoans is taken and for each individual in the sample it is determined whether they are considered a smoker. What hypothesis test is best suited for this situation?

Answer 1

Answer:

The Hypothesis test to use is the Test for Proportions.

Explanation:

There are quite a number of test to select form when analysing a statistical data. Selecting the right one can be quite tricky. When deciding which test you ought to use, there are three questions you need to answer:

1. Data (What level of measurement was used for the data being analysed?)
2. Samples (How many samples do we have?)
3. What is the purpose of the analysis?

Data

The type of data we are presented with is captured in in percentages. This is an example Nominal data.   Nominal summary values are usually stated as frequencies, proportions or percentages.

The tests that involve nominal data are:

1. Test for a proportion;
2. Difference of Two Proportions and
3. Chi Square test for independence

From the criteria above, it's clear we are dealing with Difference of Two Proportions.

Samples

This criteria begs the question: How many samples are involved?

1. Is it one sample for whose statistic (s) is being compared with a hypothetical value? or
2. Are there two sample being which are being compared with each other?
3. Is there one sample in which there is a measure or score for more than one variable? e.g. colour and grade or circumference and weight.    

From the criteria above, it's clear we have One Sample with two different considerations - Smoker or Non-smoker.

Purpose

1. Are we testing against a hypothesized value?
2. Are we comparing two statistics? or
3. Are we looking for a relationship?

You are right! From the example above, we are comparing two statistics.

Therefore putting all the criteria together, we ought to use Test for Proportions is best suited for this situation.

Cheers!

 

Answer 2

The hypothesis test that is best suited to determine the proportion of smokers in Idaho is One Proportion Test.

One Proportion Test is a hypothesis test that is used to estimate a proportion and facilitate comparison with another proportion.

One Proportion Test works by comparing the proportion to the  target/reference value.

Here, the One Proportion Test will help to compare the Idaho current samples to statistics of smoker collected in 2014.

Therefore, the Option E is correct because it is best suited to determine the proportion of smokers in Idaho is One Proportion Test.

The missing options includes "One mean, Mean of the differences, Difference of two means (independent samples), Several means (ANOVA), One proportion, Difference of two proportions, Chi-Square test of independence"

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