Questions: In a college affordability survey of 400 students in Florida, 313 students said they were offered open educational resources or free course materials. To create a 99% confidence interval using the percentile method for the population proportion (p) of college students that are offered open educational resources or free course materials, use Statkey's CI for Single Proportion under Bootstrap Confidence Intervals to create 10,000 bootstrap resamples from the original sample. 1. Use the dotplot of 10,000 bootstrap resamples you generated on StatKey to calculate the 99% confidence interval for the population proportion of college students that are offered open educational resources or free course materials. Enter your answers to 3 decimal places. 99% Confidence Interval: ( )

In a college affordability survey of 400 students in Florida, 313 students said they were offered open educational resources or free course materials. To create a 99% confidence interval using the percentile method for the population proportion (p) of college students that are offered open educational resources or free course materials, use Statkey's CI for Single Proportion under Bootstrap Confidence Intervals to create 10,000 bootstrap resamples from the original sample. 1. Use the dotplot of 10,000 bootstrap resamples you generated on StatKey to calculate the 99% confidence interval for the population proportion of college students that are offered open educational resources or free course materials. Enter your answers to 3 decimal places. 99% Confidence Interval: ( )
Transcript text: In a college affordability survey of 400 students in Florida, 313 students said they were offered open educational resources or free course materials. To create a $99 \%$ confidence interval using the percentile method for the population proportion ( $p$ ) of college students that are offered open educational resources or free course materials, use Statkey's CI for Single Proportion inder Bootstrap Confidence Intervals to create 10,000 bootstrap resamples from the original sample. 1. Use the dotplot of 10,000 bootstrap resamples you generated on StatKey to calculate the $99 \%$ confidence interval for the population proportion of college students that are offered open educational resources or free course materials. Enter your answers to 3 decimal places. 99\% Confidence Interval: ( $\square$ $\square$ )
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Solution

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Solution Steps

Step 1: Identify the sample proportion
  • The sample size (n) is 400 students.
  • The number of students offered open educational resources or free course materials is 133.
  • Calculate the sample proportion (p̂) using the formula: \[ p̂ = \frac{x}{n} = \frac{133}{400} = 0.3325 \]
Step 2: Generate bootstrap samples
  • Use statistical software or a tool like StatKey to generate 10,000 bootstrap samples from the original sample.
  • Each bootstrap sample should be of size 400, drawn with replacement from the original sample.
Step 3: Calculate the 90% confidence interval
  • Use the percentile method to find the 90% confidence interval for the population proportion.
  • In the bootstrap distribution, find the 5th percentile and the 95th percentile.
  • These percentiles represent the lower and upper bounds of the 90% confidence interval.

Final Answer

  • The 90% confidence interval for the population proportion of students offered open educational resources or free course materials is approximately [0.292, 0.375]. (Note: The exact values may vary slightly depending on the bootstrap samples generated.)
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