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Question
Math
Posted 3 months ago

A market analyst is curious what proportion of Los Angeles residents have a landline telephone. A survey of 200 randomly selected Los Angeles residents shows that 48%48 \% of those selected have a landline telephone. The analyst wants to use this data to construct a one-sample zz interval for a proportion.

Which conditions for constructing this confidence interval did their sample meet?

Choose all answers that apply:
A The data is a random sample from the population of interest.
B The observed counts of successes and failures are both sufficiently large.
C Individual observations can be considered independent.
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
Calculate the number of successes in the sample
step 2
Using the asksia-ll calculation list, the number of successes is 200×0.48=96200 \times 0.48 = 96
step 3
Calculate the number of failures in the sample
step 4
Using the asksia-ll calculation list, the number of failures is 200×(10.48)=104200 \times (1 - 0.48) = 104
step 5
Determine if the sample size is large enough for both successes and failures
step 6
Since both the number of successes (96) and failures (104) are greater than 5, the sample size condition is met
Answer
The conditions for constructing this confidence interval that their sample met are A, B, and C.
Key Concept
Conditions for Constructing a Confidence Interval
Explanation
For a one-sample zz interval for a proportion, the sample must be random (A), and both the observed counts of successes and failures must be sufficiently large (B), typically at least 5. Additionally, individual observations should be independent (C), which is generally assumed for a random sample. In this scenario, all conditions are met.

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