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Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want 90​% confidence that your error is no more than 0.05.

The sample should include how many men and how many women?

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JeanaShupp

Answer: The sample should include 542 men and 542 women.

Step-by-step explanation:

When the prior estimate of the population proportion for both population 1 and population 2 are not available , then we assume that it 0.5 i.e. both have equal chances.

Formula to find the equal sample sizes : [tex]n_1=n_2=\dfrac{(z^*)^2}{2E^2}[/tex] , where z* = critical z-values associated with the given confidence level and E = Margin of error.

By considering the given information , we have

E= 0.05

Confidence level = 90% =0.90

Critical z-value for 90% confidence level : z*=1.645 (By z-table)

Now, the required sample sizes would be :

[tex]n_1=n_2=\dfrac{(1.645)^2}{2(0.05)^2}\\\\=\dfrac{2.706025}{2\times0.0025}=541.205\approx542[/tex]

Hence, the sample should include 542 men and 542 women.

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