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Math  /  Data & Statistics

Questiona. In testing the common belief that the proportion of male babies is equal to 0.512 , identify the values of p^\hat{p} and pp. p^=\hat{p}= □\square p=\mathrm{p}= □\square (Round to three decimal places as needed.) (Round to three decimal places as needed.) A. Those that are both grester than or equal to □\square and less than or equal to □\square B. Those that are greater than or equal to □\square C. Those that are less than or equal to □\square D. Those that are less than or equal to □\square and those that are greater than or equal to □\square -
There □\square sufficient evidence to □\square the claim that the proportion of male births is equal to 0.512 .

Studdy Solution

STEP 1

1. p^\hat{p} represents the sample proportion of male births.
2. pp represents the hypothesized population proportion of male births.
3. The sample consists of 880 births with 426 male births.
4. The hypothesized proportion pp is given as 0.512.

STEP 2

1. Calculate the sample proportion p^\hat{p}.
2. Identify the hypothesized population proportion pp.
3. Determine sample proportions at least as extreme as the observed sample proportion.
4. Evaluate the evidence to support or reject the claim using a significance level of 0.05.

STEP 3

Calculate the sample proportion p^\hat{p}:
p^=Number of male birthsTotal number of births=426880\hat{p} = \frac{\text{Number of male births}}{\text{Total number of births}} = \frac{426}{880}
Calculate p^\hat{p} to three decimal places:
p^=426880≈0.484\hat{p} = \frac{426}{880} \approx 0.484

STEP 4

Identify the hypothesized population proportion pp:
p=0.512p = 0.512

STEP 5

Determine which sample proportions are at least as extreme as the observed sample proportion p^=0.484\hat{p} = 0.484. This involves comparing p^\hat{p} to the hypothesized proportion p=0.512p = 0.512.
- Option A: Those that are both greater than or equal to □\square and less than or equal to □\square - Option B: Those that are greater than or equal to □\square - Option C: Those that are less than or equal to □\square - Option D: Those that are less than or equal to □\square and those that are greater than or equal to □\square
Since p^<p\hat{p} < p, we consider sample proportions less than or equal to p^\hat{p}.

STEP 6

Evaluate the evidence using a randomization method with 1000 resamples and a significance level of 0.05.
- If the proportion of resamples with a sample proportion as extreme or more extreme than p^\hat{p} is less than 0.05, there is sufficient evidence to reject the claim. - Otherwise, there is not sufficient evidence to reject the claim.
The values are: p^=0.484\hat{p} = 0.484 p=0.512p = 0.512

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