Question

Difficulty: HardStatistical Sampling and Studies

A sociologist is studying the print newspaper subscription habits of residents in a city. The table below shows the total number of households, the sample size, and the number of households in each sample that report subscribing to a print newspaper for the city's two districts.

DistrictTotal householdsSample sizeSubscribing households in sample
West10,00010,0002002003535
East14,00014,0002502506060

Based on the results of these samples, what is the estimated total number of households in the city that subscribe to a print newspaper?

Answer: 5110

Answer

5110
To find the total estimated number of households in the city that subscribe to a print newspaper, we must estimate the subscriptions for each district separately and then sum them. For District West, the proportion of households subscribing is 35200=0.175\frac{35}{200} = 0.175. Multiplying this by the total number of households in District West (10,00010,000) gives an estimate of 1,7501,750 subscribing households. For District East, the proportion of households subscribing is 60250=0.24\frac{60}{250} = 0.24. Multiplying this by the total number of households in District East (14,00014,000) gives an estimate of 3,3603,360 subscribing households. Adding these two estimates together (1,750+3,3601,750 + 3,360) results in a total estimate of 5,1105,110 households.

Step-by-Step Solution

1
Calculate the estimated number of print newspaper subscriptions in District West.
1,750 households
The proportion of subscribing households in the District West sample is applied to the total number of households in District West.
2
Calculate the estimated number of print newspaper subscriptions in District East.
3,360 households
The proportion of subscribing households in the District East sample is applied to the total number of households in District East.
3
Find the total estimated number of subscribing households in the city.
5,110 households
Adding the estimates from both districts yields the overall population estimate.

Key Concept

Estimating population parameters from stratified random samples
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