Based on a random sample of 1040 adults, the mean amount of sleep per night is...

Based on a random sample of 1040 adults, the mean amount of sleep per night is 8.26 hours. Assuming the population standard deviation for the amount of sleep per night is 2.7 hours, construct and interpret a 95% confidence interval for the mean amount of sleep per night.

A 95% confidence interval is (, ) Interpret the confidence interval.

Interpret the confidence Interval:

A. We are 95% confident that the interval actually does contain the true value of the mean.

B. There is a 95% chance that the true value of the mean will not equal the mean of the interval.

C. There is a 95% chance that the true value of the mean will equal the mean of the interval.

D. We are 95% confident that interval actually does not contain the true value of the man.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 8.26

Population standard deviation = = 2.7

Sample size = n = 1040

Z_/2 = 1.96

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 1.96 * (2.7 / $\sqrt$ 1040)

= 0.16

At 95% confidence interval estimate of the population mean is,

- E < < + E

8.26 - 0.16 < < 8.26 +0 16

8.10 < < 8.42

(8.10 , 8.42)

A. We are 95% confident that the interval actually does contain the true value of the mean.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A researcher calculated average sleep hours per night for a random sample of (n= 5454) students....

A researcher calculated average sleep hours per night for a random sample of (n= 5454) students. The researcher hypothesised that a healthy person is expected to sleep 8.58.5 hours per night (μ0=8.5μ0=8.5). The sample mean y¯y¯ is equal to 8.28.2 hours and the sample variance s2n−1sn−12 is equal to 1.181.18 hours. Research Question: Is the average hours of sleep equal to hypothesised hours of sleep per night? Answer the following questions by choosing the most correct option or typing the...

A researcher calculated average sleep hours per night for a random sample of (n= 4646) students....

A researcher calculated average sleep hours per night for a random sample of (n= 4646) students. The researcher hypothesised that a healthy person is expected to sleep 88 hours per night (μ0=8μ0=8). The sample mean y¯y¯ is equal to 7.97.9 hours and the sample variance s2n−1sn−12 is equal to 1.241.24 hours. Research Question: Is the average hours of sleep equal to hypothesised hours of sleep per night? Answer the following questions by choosing the most correct option or typing the...

Suppose that in a large population of students, the mean amount of sleep the previous night...

Suppose that in a large population of students, the mean amount of sleep the previous night was μ = 7.15 hours and the standard deviation was σ = 1.5 hours. Consider randomly selected samples of n = 240 students. (a) What is the value of the mean of the sampling distribution of possible sample means? Mean = (b) Calculate the standard deviation, s.d., of the sampling distribution of possible sample means. (Round your answer to three decimal places.) s.d.(x) =...

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical option

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow....

a) The average nightly sleep time for adults is 7.4 hours a night with a standard...

a) The average nightly sleep time for adults is 7.4 hours a night with a standard deviation of 2.3 hours. A researcher suspects that college students’ sleep time may vary from this average. She surveys a sample of 12 college students and obtains the following nightly sleep times for this sample: Participant/Sleep Time (hours) A - 3 B - 4.5 C - 9 D - 7 E - 8 F - 5 G - 6 H - 4 I -...

The Sleep Heart Health Study enrolled a simple random sample of 688 adults not treated for...

The Sleep Heart Health Study enrolled a simple random sample of 688 adults not treated for sleep-disordered breathing. The men and women in the study were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). We will use a chi-square test to test the competing hypotheses: H0: There is no association between the severity of sleep-disordered breathing and sex versus H1: There is some association between the severity of sleep-disordered breathing and...

The National Sleep Foundation used a survey to determine whether hours of sleep per night are...

The National Sleep Foundation used a survey to determine whether hours of sleep per night are independent of age (Newsweek, January 19, 2004). A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age...

1.) 25 Pittsburgh residents were asked how much sleep they get per night. The mean was...

1.) 25 Pittsburgh residents were asked how much sleep they get per night. The mean was 7.2 hours and the standard deviation was 0.78 hours. Construct and interpret a 90% confidence interval for the true mean number of hours of sleep that Pittsburgh residents get per night. 2.) A sample of 11 Chevy Volt drivers resulted in them having a mean of 42.6 miles per gallon (mpg) and a standard deviation of 4.8 mpg. Construct and interpret a 95% confidence...

Sleep: Assume the general population gets an average of 7 hours of sleep per night. You...

Sleep: Assume the general population gets an average of 7 hours of sleep per night. You randomly select 45 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.89 hours with a standard deviation of 0.25 hours. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less...

A random sample of 500 male and female adults was asked the amount of time each...

A random sample of 500 male and female adults was asked the amount of time each person spent watching TV last week. Their responses are shown at the right. At the 0.05 significance level, does it appear that the amount of time spent watching TV is related to the gender of the viewer? Hours/Gender Male Female Total Under 8 90 110 200 8 to 15 85 75 160 15 or more 75 65 140 Total 250 250 500 Which test...

Subjects