6. For a town of 50,000 households, the average number of persons age 16 and ove

Question

6. For a town of 50,000 households, the average number of persons age 16 and oveer living in each household is known to be 2.38, with a standard deviation of 1.87. A survey organization plans to take simple random sample of 400 households, and interview all persons age 16 sand over living in the sample households. Complete the following statements with the appropriate values. (a) The total number of interviews will be around_____ give or take _____or so. (b) The chance that there will be exactly one thousand interviews is =_______.(Please be sure to use the Standard Normal Density Chart, if applicable)

Explanation / Answer

a) Total households = 50,000, mean = 2.38, Standard deviation = 1.87, Sample size = 400

The total no. of interviews of persons aged 16 and above will be around 400 * 2.38 = 952.

The standard error for the sum of people greater than 16 years is sqrt(sample size) * standard deviation

standard error = sqrt(400) * 1.87 = 37.4

hence we should expect in a sample of 400 households, 952 people to be above 16 give or take 37 or so.

b) If there are exactly 1000 interviews, then the no. of interviews per household = 1000/400 = 2.5

The chance that there will be exactly 1000 interviews can be found out by calculating the density of the normal distribution at value 2.5, with mean = 2.38 and sd = 1.87

dnorm(2.5, mean = 2.38, sd = 1.87)

= 0.2128993

So chances are around 21.3%

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