MATH 225N WEEK 5 ASSIGNMENT: CENTRAL LIMIT THEOREM FOR PROPORTIONS

MATH 225N WEEK 5 ASSIGNMENT: CENTRAL LIMIT THEOREM FOR PROPORTIONS

1.  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.

Correct answers:

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

2.   From recent census data, it is discovered that the proportion of the adults in the United States who are first generation Americans is 14%. For a random sample of size 500, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

---Given the population proportion p=14%=0.14 and a sample size of n=500, the standard deviation of the sampling distribution of sample proportions is

σpˆ=p(1−p)n−−−−−−−√=0.14(1−0.14)500−−−−−−−−−−−−√≈0.016

3.   From recent survey data, a car buying business finds that 12.5% of the proportion of adults in a city would be likely to use their services. For a random