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A random sample of 68 households was selected for a phone survey. The key question asked​ was, "Do you or any member of your household own a product from Company​ A?" Of the 68 ​respondents, 34 said yes and 34 said no. a. Determine the sample​ proportion, p, of households that own a Company A product. b. If the population proportion is 0.75​, determine the standard error of the proportion.

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Answer:

a. p = 0.5

b. SE = 0.0525

Step-by-step explanation:

a. The sample proportion (p) of households that own a Company A product is given by the number of people who answered "yes"(34) divided by the sample size (n=68)

[tex]p = \frac{34}{68}=0.5[/tex]

The sample proportion is 0.5.

b. If the population proportion is P = 0.75, the standard error is given by:

[tex]SE=\sqrt{\frac{P*(1-P)}{n}}\\SE=\sqrt{\frac{0.75*(1-0.75)}{68}}\\ SE=0.0525[/tex]

The standard error is 0.0525.

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