The school superintendent would like to estimate the proportion of adults in the country that are in favor of an increased emphasis on the basics of education. A randomly selected sample of 150 adults found that 107 of them would favor an increased emphasis on basics of education. Find a 90% lower estimate of the proportion of county of adults that favor an increased emphasis.

To find the 90% lower estimate of the proportion of adults in the country that favor an increased emphasis on the basics of education, you can use a confidence interval formula.

The formula for a confidence interval of a proportion is:

Confidence Interval = Sample Proportion ± (Critical Value) × (Standard Error)

In this case, the sample proportion is 107/150, as 107 out of 150 adults in the sample favor an increased emphasis. The critical value depends on the desired level of confidence. Since we want a 90% lower estimate, we need to find the critical value that corresponds to a 90% confidence level.

The standard error is calculated as the square root of (Sample Proportion × (1 - Sample Proportion) ÷ Sample Size). So, in this case, the standard error is the square root of (107/150 × (1 - 107/150) ÷ 150).

Once you have the critical value and the standard error, you can calculate the confidence interval by subtracting (Critical Value × Standard Error) from the sample proportion.

Here are the steps to find the 90% lower estimate of the proportion of adults that favor an increased emphasis on the basics of education:

Step 1: Calculate the sample proportion.
Sample Proportion = number of adults who favor an increased emphasis / total sample size
Sample Proportion = 107/150

Step 2: Calculate the standard error.
Standard Error = √(Sample Proportion × (1 - Sample Proportion) ÷ Sample Size)
Standard Error = √((107/150) × (1 - 107/150) ÷ 150)

Step 3: Determine the critical value for a 90% confidence level.
The critical value depends on the desired level of confidence. For a 90% confidence level, it corresponds to a one-tailed z-test. Using statistical tables or software, you can find that the critical value is approximately 1.645.

Step 4: Calculate the confidence interval.
Confidence Interval = Sample Proportion - (Critical Value × Standard Error)
Confidence Interval = (107/150) - (1.645 × √((107/150) × (1 - 107/150) ÷ 150))

By performing these calculations, you will obtain the lower estimate of the proportion of adults in the country that favor an increased emphasis on the basics of education with a 90% confidence level.