(Solution) Math 225N Week 5 Assignment Central Limit Theorem for proportions

Week 5 Assignment Central Limit Theorem for proportions

Question

A dental student is conducting a study on the number of people who visit their dentist regularly. Of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=60.

 

Question

Of the 13,500 savings accounts in a bank, 4,675 belong to people younger than 40 years old. The bank president would like to increase her institution’s marketing strategy to younger customers, so she is examining the population proportions in order to create a statistical study.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=400.

 

Question

A baseball team calls itself “America’s Favorite Team,” because it has 90,000 fans on social media out of 2,210,000 social media users.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=1,000.

The population proportion is p=90,0002,210,000≈0.041. This is also the mean of the sampling distribution:

Question

A study by doctors of children attending a certain elementary school finds that, of 812 students, 245 watch more than 2 hours of television each day.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=100 students.

 

Solutions:

Question

A dental student is conducting a study on the number of people who visit their dentist regularly. Of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=60.

The population proportion is p=312520≈0.600. This is also the mean of the sampling distribution:

μp^=p=0.600

For samples of size n=60, the standard deviation of the sampling distribution is

σpˆ=p(1−p)n−−−−−−−√=0.600(1−0.600)60−−−−−−−−−−−−−−√≈0.063

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