Solve the Problem $\mathrm { P } _ { 1 } \not \subset \mathrm { P } 2$

question 127

Multiple Choice

Solve the problem.
-The table shows the number of smokers in a random sample of 500 adults aged 20-24 and the number of smokers in a random sample of 450 adults aged 25-29. Assume that you plan to use a significance level of
Α = 0.10 to test the claim that $\mathrm { P } _ { 1 } \not \subset \mathrm { P } 2$ Find the critical value(s) for this hypothesis test. Do the data provide
Sufficient evidence that the proportion of smokers in the 20-24 age group is different from the proportion of
Smokers in the 25-29 age group? $\begin{array}{lcc}\hline & \text { Age 20-24 } & \text { Age 25-29 } \\\hline \text { Number in sample } & 500 & 450 \\\text { Number of smokers } & 110 & 63 \\\hline\end{array}$

• A) \(z = \pm 1.28\); yes
• B) \(\mathrm { z } = \pm 1.645\); yes
• C) \(\mathrm { z } = \pm 1.96\); no
• D) \(\mathrm { z } = 1.28\); no

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Definitions:

Standard Deviation

A measure of the dispersion or spread of a set of data points from its mean, indicating how much variation exists from the average.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values in a dataset deviate from the mean.

Nonconforming Items

Products or outputs that do not meet the specified standards or quality criteria.

Samples

Selected portions or subsets of a population, used in statistical analysis to estimate characteristics of the whole population.