Question

In: Statistics and Probability

You are interested in estimating the the mean age of the citizens living in your community....

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 25 years.

Sample Size: ______

Expert Solution

A % CI for mean can be obtained using the formula:

where, is the margin of Error.

From the above formula, n can be computed as:

Given: and critical value for Z for can be obtained from standard normal table, looking for area :

We get Z_critical = 2.17

Substituting the values:

= 183.9414

We get, Sample size = 184

orchestra answered 1 year ago

1.You are interested in estimating the the mean weight of the local adult population of female...

1.You are interested in estimating the the mean weight of the local adult population of female white-tailed deer (doe). From past data, you estimate that the standard deviation of all adult female white-tailed deer in this region to be 21 pounds. What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 98% confidence level, to within 9 pounds of the actual weight? 2.You measure 30 backpacks' weights, and find...

A researcher specializing in the area of juvenile delinquency is interested in estimating the average age...

A researcher specializing in the area of juvenile delinquency is interested in estimating the average age when delinquency first begins. Taking a random sample of 57 juveniles, she determines a sample mean of 13.4 years and a sample standard deviation of 1.5 years. Construct a 99% confidence interval to estimate when the average population (mean) age of delinquency begins

A community living on an island off the west coast of Scotland is interested in meeting...

A community living on an island off the west coast of Scotland is interested in meeting its electricity needs using marine renewable energy. Critique the standard approach for assessing the resource potential of wave power around the island, as included in the course notes. Include in your answer the main assumptions of the approach, its limitations and suggestions for improving its accuracy. [

the owner of a fitness center is interested in estimating the difference in mean years that...

the owner of a fitness center is interested in estimating the difference in mean years that female members have been with the club compared with male members. he wishes to develop a 99% confidence interval estimate. The data are showen in the accompanying table. Assuming that the same data are approximately normal and that the two populations have equal variances, develop and interpret the confidence interval estimate. dicuss the results gender 1=male 2=female 1 2 2 2 1 2 2...

The owner of a fitness center is interested in estimating the difference in mean years that...

The owner of a fitness center is interested in estimating the difference in mean years that female members have been with the club compared with male members. He wishes to develop a 95% confidence interval estimate. The data are shown in the accompanying table. Assuming that the sample data are approximately normal and that the two populations have equal variances, develop and interpret the confidence interval estimate. Discuss the result. Gender_(1=Male_2=Female) Years_With_the_Club 2 3.5 2 1 1 3 2 2...

A community health association is interested in estimating the average number of maternity days women stay...

A community health association is interested in estimating the average number of maternity days women stay in the local hospital. A random sample is taken of 36 women who had babies in the hospital during the past year. The following numbers of maternity days each woman was in the hospital are rounded to the nearest day. 3 3 4 3 2 5 3 1 4 3 4 2 3 5 3 2 4 3 2 2 1 6 3 4...

A large Midwestern university is interested in estimating the mean time that students spend at the...

A large Midwestern university is interested in estimating the mean time that students spend at the student recreation center per week. A previous study indicated that the standard deviation in time is about 25 minutes per week. If the officials wish to estimate the mean time within ± 4 minutes with a 90 percent confidence, what should the sample size be? 106 Can't be determined without the sample mean. 105 105.685

3) Suppose you know the true mean GPA of Howard Community College and are interested in...

3) Suppose you know the true mean GPA of Howard Community College and are interested in seeing how students in your stats class compare to the college average. Compared to the sampling distribution of the means for small samples (say n = 4), how will the sampling distribution of the means be different for larger samples (say n = 25)? a.) The sampling distribution for n=25 will have a larger mean b.) The sampling distribution for n=25 will have a...

An insurance company is interested in estimating the population mean cost of basic dental cleaning at...

An insurance company is interested in estimating the population mean cost of basic dental cleaning at dentists in Saskatoon. Suppose there are only two dentists in Saskatoon: Dentist A and Dentist B. Suppose also that the cost of basic dental cleaning varies only depending on how well the patient practices regular dental hygiene, so that the cost of basic dental cleaning roughly follows a Normal distribution regardless of the dentist. The insurance company selects 8 sample patients and sends them...

An educational organization in California is interested in estimating the mean number of minutes per day...

An educational organization in California is interested in estimating the mean number of minutes per day that children between the age of 6 and 18 spend watching television per day. A previous study showed that the population standard deviation was 21.5 minutes. The organization selected a random sample of n = 251 children and recorded the number of minutes of TV that each person watched on a particular day. The mean time was 171.3 minutes. If the leaders of the...