IHP 525 Quiz Threea Sample Of 49 Sudden Infant Death Syndrom

Ihp 525 Quiz Threea Sample Of 49 Sudden Infant Death Syndrome Sids C

IHP 525 Quiz Three A sample of 49 sudden infant death syndrome (SIDS) cases had a mean birth weight of 2998 g. Based on other births in the county, we will assume σ = 800 g. Calculate the 95% confidence interval for the mean birth weight of SIDS cases in the county. Interpret your results.

Given that a confidence interval for μ is 13 ± 5. The value of 13 in this expression is the point estimate. The value 5 in this expression is the margin of error. The width of the confidence interval is 10. The value 5 is not the standard error of the estimate.

When do we use a t-statistic instead of a z-statistic to help infer a mean? Usually, a t-statistic is used when the sample size is small (n

Identify whether the studies described here are based on (1) single samples, (2) paired samples, or (3) independent samples:

• Cardiovascular disease risk factors are compared in husbands and wives. - (3) independent samples
• A nutritional exam is applied to a random sample of individuals. Results are compared to the results of the whole nation. - (1) single samples for the group, but comparison made to a known population.
• An investigator compares vaccination histories in 30 autistic schoolchildren to a simple random sample of non-autistic children from the same school district. - (3) independent samples

Identify two graphical methods that can be used to compare quantitative (continuous) data between two independent groups:

• Side-by-side boxplots
• Histograms or density plots for each group overlaid for comparison

The data for boys: {72, 73, 86, 95, 95, 95, 96, 97, 99, 125}.

The data for girls: {89, 92, 93, 98, 105, 106, 110, 126, 127, 130}.

Explore the group differences with side-by-side boxplots. Based on the boxplots and data, risk-taking behavior appears to be higher among girls, with median and upper quartile values greater than those for boys, and some outliers in girls indicating higher scores.

The sample size required for a study with 90% power will be larger than that for 80% power when all other factors (population, expected difference, variation, α) remain constant, since higher power requires a larger sample to detect the same effect size reliably.

True or False: When using data from the same sample, the 95% confidence interval for μ will always support the results from a 2-sided, 1-sample t-test. - False. The confidence interval provides a range of plausible values for μ, but it may not always include the value tested by the t-test, especially if the sample size is small or the data are skewed.

Paper For Above instruction

Confidence intervals and hypothesis testing are fundamental concepts in inferential statistics, enabling researchers to make informed conclusions about populations based on sample data. In this context, calculating a 95% confidence interval for the mean birth weight of infants who experienced sudden infant death syndrome (SIDS) provides insights into the typical birth weight within this vulnerable group and aids in understanding potential risk factors associated with SIDS.

Given a sample of 49 SIDS cases with a mean birth weight of 2998 grams and a known population standard deviation (σ) of 800 grams, we can compute the confidence interval using the z-distribution. The formula for the confidence interval is:

CI = x̄ ± Z_α/2 * (σ / √n)

where x̄ is the sample mean, Z_α/2 is the critical value from the standard normal distribution for a 95% confidence level, σ is the population standard deviation, and n is the sample size.

At a 95% confidence level, Z_α/2 is approximately 1.96. Substituting the values:

CI = 2998 ± 1.96 * (800 / √49)

Because √49 = 7, the standard error (SE) = 800 / 7 ≈ 114.29. Therefore:

CI = 2998 ± 1.96 * 114.29 ≈ 2998 ± 223.86

Thus, the 95% confidence interval is approximately (2774.14 g, 3221.86 g).

This interval indicates that, with 95% confidence, the true mean birth weight for all SIDS infants in the county falls within this range. Since the interval is broad, reflecting the variability and the known population standard deviation, it provides a useful estimate for clinicians and public health officials to understand the typical birth weights among SIDS cases. The lower bound suggests that some infants may have relatively low birth weights, highlighting a potential area for intervention or further research.

Regarding the statement about confidence intervals and t-tests, the claim that the 95% confidence interval always supports the results of a two-sided, one-sample t-test when using data from the same sample is false. While these two methods are related and often lead to similar conclusions, differences can occur, especially with small samples or non-normal data distributions. Confidence intervals provide a range of plausible values for the population mean, while a t-test assesses whether there is a statistically significant difference from a hypothesized value. When sample sizes are small, the t-distribution accounts for extra variability, whereas the confidence interval relies on the same t-distribution to derive its bounds. Therefore, the conclusions from a t-test and a confidence interval are consistent but not always supportive of each other explicitly, especially under certain data conditions.

Furthermore, understanding the use of the t-statistic versus the z-statistic highlights critical considerations in statistical inference. The z-statistic is appropriate when the population standard deviation is known, and the sample size is sufficiently large (commonly n ≥ 30), as in the initial SIDS example. Conversely, when the population standard deviation is unknown and the sample size is small, the t-statistic offers a more accurate inference by incorporating the sample standard deviation and degrees of freedom.

Comparative study designs, such as those involving paired or independent samples, influence the type of analysis performed. The example comparing cardiovascular risk factors in husbands and wives involves paired samples because measurements are linked within couples. The study on vaccination histories in autistic children versus non-autistic children involves independent samples, as the groups are separate. Graphical methods like side-by-side boxplots and density plots provide visual comparison tools for analyzing differences in quantitative data between independent groups. These visualizations can reveal differences in central tendency, variability, and potential outliers, aiding in interpretation before formal statistical testing.

Finally, examining the risk-taking scores among boys and girls demonstrates how visualization and descriptive statistics help uncover gender differences. The boxplots reveal that girls tend to have higher median and upper quartile scores, indicating a tendency toward more risk-taking behavior, with potential outliers reflecting extreme scores. When planning future research, power analysis guides sample size determination to detect specified differences with desired certainty. Increasing the power from 80% to 90% generally necessitates a larger sample size, reflecting the balance between statistical sensitivity and resource allocation.

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