Understanding Confidence Intervals and Sampling

The video tutorial explains a survey conducted in a teaching district to assess teachers' views on computers as essential teaching tools. It covers the calculation of a 99% confidence interval for the proportion of teachers who find computers essential, using sample data. The tutorial details the process of calculating sample proportion, variance, and standard deviation, and explains the use of a Z-table to determine confidence intervals. It concludes with suggestions for improving the survey by increasing sample size to narrow the confidence interval.

What was the purpose of the technology grant mentioned in the video?

• To provide internet access to all students

• To install a cluster of four computers in classrooms

• To train teachers in using new software

• To build new classrooms

How many teachers were surveyed to determine the importance of computers as a teaching tool?

• 250

• 500

• 142

• 6,250

In the context of the video, what does a '1' represent in the Bernoulli Distribution?

• A teacher who thinks computers are essential

• A teacher who thinks computers are not essential

• A teacher who is undecided

• A teacher who has not used computers

What is the sample proportion of teachers who believe computers are essential?

• 0.031

• 0.568

• 0.246

• 0.50

What is the purpose of calculating the sample variance in the video?

• To determine the average age of teachers

• To estimate the true variance for building a confidence interval

• To find the number of teachers who dislike computers

• To calculate the total number of computers needed

What is the estimated standard deviation of the sampling distribution in the video?

• 0.568

• 0.246

• 0.50

• 0.031

How many standard deviations away from the mean are needed for a 99% confidence interval?

• 2.58

• 2.5

• 3.0

• 1.96

What is the range of the 99% confidence interval for the proportion of teachers who think computers are essential?

• 0.246 to 0.568

• 0.031 to 0.50

• 0.568 to 0.648

• 0.488 to 0.648

What is one way to narrow the confidence interval while maintaining the same confidence level?

• Change the survey questions

• Use a different confidence level

• Increase the sample size

• Decrease the sample size

Why does increasing the sample size narrow the confidence interval?

• It increases the standard deviation

• It changes the mean

• It alters the Z-score

• It decreases the standard deviation