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 $48 \%$ of those selected have a landline telephone. The analyst wants to use this data to construct a one-sample $z$ 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.
```

Sign in to unlock the answer

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 $200 \times 0.48 = 96$

step 3

Calculate the number of failures in the sample

step 4

Using the asksia-ll calculation list, the number of failures is $200 \times (1 - 0.48) = 104$

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 $z$ 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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question