Confidence Intervals (Mean)

Question 1

Assume that a sample is used to estimate a population mean u. Find the 80% confidence interval for a sample of size 633 with a mean of 78.1 and a standard deviation of 21.3. Enter your answer as a trilinear inequality accurate to 3 decimal places.

Question 2

Assume that a sample is used to estimate a population mean u . Find the 99.5% confidence interval for a sample of size 1000 with a mean of 38.4 and a standard deviation of 21.9. Enter your answer as a trilinear inequality accurate to 3 decimal places.

Question 3

Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 41 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 19.5 and a standard deviation of 3.7. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

Question 4

A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 71 specimens and counts the number of seeds in each. Use her sample results (mean = 40.9, standard deviation = 5.2) to find the 99% confidence interval for the number of seeds for the species. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.

Question 5

In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42.3 and standard deviation of $13.3. Estimate how much a typical parent would spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.

Question 6

A researcher is interested in finding a 98% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 95 students who averaged 38.8 minutes concentrating on their professor during the hour lecture. The standard deviation was 12.4 minutes.

a. To compute the confidence interval use a distribution.

b. With 98% confidence the population mean minutes of concentration is between ______  and ______  minutes.

c. If many groups of 95 randomly selected members are studied, then a different confidence interval would be produced from each group. About______ percent of these confidence intervals will contain the true population mean minutes of concentration and about ______  percent will not contain the true population mean minutes of concentration. 

Question 7

A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 252 members were looked at and their mean number of visits per week was 3.5 and the standard deviation was 1.6. Round answers to 3 decimal places where possible. 

a. To compute the confidence interval use a distribution.

b. With 90% confidence the population mean number of visits per week is between ______   and______ visits.

c. If many groups of 252 randomly selected members are studied, then a different confidence interval would be produced from each group. About______ percent of these confidence intervals will contain the true population mean number of visits per week and about ______ percent will not contain the true population mean number of visits per week. 

Question 8

A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 214 members were looked at and their mean number of visits per week was 3.3 and the standard deviation was 2.7.

a. To compute the confidence interval use a distribution.

b. With 90% confidence the population mean number of visits per week is between______  and ______  visits.

c. If many groups of 214 randomly selected members are studied, then a different confidence interval would be produced from each group. About ______  percent of these confidence intervals will contain the true population mean number of visits per week and about______ percent will not contain the true population mean number of visits per week. 

Question 9

The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:

96.4 97.2 99.2 98.6 98.3 99.4 99.6 98.1

Assume body temperatures of adults are normally distributed. Based on this data, find the 95% confidence interval of the mean body temperature of adults in the town. Enter your answer as an openinterval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population. 

Question 10 

The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:

98.6 99.9 96.6 98.5 96.8 97.6 96.5 98.8 96.3 96.7 98.7

Assume body temperatures of adults are normally distributed. Based on this data, find the 98% confidence interval of the mean body temperature of adults in the town. Enter your answer as an openinterval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population. 

Question 11

You are interested in finding a 98% confidence interval for the average commute that nonresidential students have to their college. The data below show the number of commute miles for 13 randomly selected non-residential college students.

13 18 24 7 7 23 6 19 7 9 23 16 5

a. To compute the confidence interval use a distribution.

b. With 98% confidence the population mean commute for non-residential college students is between ______and ______miles.

c. If many groups of 13 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About______ percent of these confidence intervals will contain the true population mean number of commute miles and about ______percent will not contain the true population mean number of  commute miles. 

Question 12

A psychiatrist is interested in finding a 95% confidence interval for the tics per hour exhibited by children with Tourette syndrome. The data below show the tics in an observed hour for 15 randomly selected children with Tourette syndrome. Round answers to 3 decimal places where possible. 

8 5 12 6 8 2 0 6 9 9 3 3 4 3 4

a. To compute the confidence interval use a distribution.

b. With 95% confidence the population mean number of tics per hour that children with Tourette syndrome exhibit is between _____and_____.

c. If many groups of 15 randomly selected  children with Tourette syndrome are observed, then a different confidence interval would be produced from each group. About _____percent of these confidence intervals will contain the true population mean number of tics per hour and about _____percent will not contain the true population mean number of tics per hour. 

Question 13

You are interested in finding a 90% confidence interval for the average number of days of class that college students miss each year. The data below show the number of missed days for 11 randomly selected college students. Round answers to 3 decimal places where possible.

10 5 5 10 11 2 5 10 9 12 4

a. To compute the confidence interval use a distribution.

b. With 90% confidence the population mean number of days of class that college students miss is between _____and _____days.

c. If many groups of 11 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About_____ percent of these confidence intervals will contain the true population mean number of missed class days and about_____ percent will not contain the true population mean number of missed class days.