Question

For this project you will estimate parameters using confidence intervals. For each confidence interval, make sure you report  

• The confidence interval limits rounded as directed (Use StatCrunch to find all confidence interval limits. Use Stat>Proportion Stats to find confidence interval limits for proportions. Use Stat>T Stats to find confidence interval limits for means.) Refer to the resources on the course home page for more information about confidence intervals and how to find them using StatCrunch.
• An interpretation of the confidence interval.

Here is a template for reporting the answer for a sample problem.

Sample problem:

Find a 95% confidence interval for the proportion of all people who use their smart phones to watch movies.

Related Question: Does it appear 50% of all people use their smart phones for watching movies?

Interval Limits: 0.255 to 0.488

Interpretation: "I am 95% confident the interval from 0.255 to 0.488 contains the true value of the population proportion of people who use their smart phone to watch movies."

Related Question Answer: No, because 0.50 does not fall within the interval limits, therefore, 50% is not a plausible value for the proportion of all people who use their smarth phones to watch movies.

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Use the class data to find the confidence intervals described below. Type your answers in a Microsoft Word or rich text format document making sure you clearly show your answers for each problem and upload your document to submit your work. Use the Grapevine Online Statistics Data File in StatCrunch shared by user sgrapevine. Assume this data is representative of all online students. Round the interval limits as directed. Each problem is worth a total of 6 points (2 points for reporting the correct confidence interval limits, 2 points for providing a correct interpretation of the confidence interval, 1 point for answering the related question, and 1 point for explaining why or why not for each related question). You can also earn 1 point for rounding as directed for a total of 43 points. Note, this is not a team project. You must submit your own original work!

1) Find a 90% confidence interval for the mean hours of sleep online students typically get on a weekendnight. Round the interval limits to the nearest tenth.

Related Question: Is there strong evidence the average online student gets more than 7 hours of sleep on a weekend night? Why or why not?

2) Find a 95% confidence interval for the proportion of all online students that will call "heads" will given the option to call a coin toss. Round the interval limits to the nearest thousandth.

Related Question: Is it plausible that heads and tails are called equally when online students are asked to call a coin toss? Why or why not?

3) Find a 99% confidence interval for the mean foot length for all online students. Round the interval limits to the nearest tenth.

Related Question: Is there strong evidence the average foot length for all online students is different from 25 cm? Why or why not?

4) Find a 95% confidence interval for the mean number of letters in the last names of all online students. Round the interval limits to the nearest tenth.

Related Question: Is there strong evidence the average online student have a last name length of less than 10 letters? Why or why not?

5) Find a 90% confidence interval for the proportion of all online students who think dogs are the best pet. Round the interval limits to the nearest thousandth.

Related Question: Does it appear a majority (over 50%) of all online students think dogs make the best pet? Why or why not?

6) Find a 99% confidence interval for the proportion of all online students that pick the number 3 when asked to pick a number between 1 and 5. Round the interval limits to the nearest thousandth.

Related Question: Does it appear all online students select numbers randomly, that is, in this situation, is there strong evidence every number including the number 3 has the same 20% chance of being selected? Why or why not?

7) Find a 95% confidence interval for the proportion of all online students that have brown eyes. Round the interval limits to the nearest thousandth.

Related Question: Is it plausible 25% of all online students have brown eyes? Why or why not?

Answer 1

2) Find a 95% confidence interval for the proportion of all online students that will call "heads" will given the option to call a coin toss. Round the interval limits to the nearest thousandth.

Related Question: Is it plausible that heads and tails are called equally when online students are asked to call a coin toss? Why or why not?

Interval Limits:

When a fair coin was tossed, 21 out of the 35 students called Heads.

n = 35    

p = 21/35 = 0.6    

% = 95    

Standard Error, SE = √{p(1 - p)/n} =    √(0.6(1 - 0.6))/35 = 0.082807867

z- score = 1.959963985    

Width of the confidence interval = z * SE =     1.95996398454005 * 0.0828078671210825 = 0.16230044

Lower Limit of the confidence interval = P - width =     0.6 - 0.1623004371939 = 0.43769956

Upper Limit of the confidence interval = P + width =     0.6 + 0.1623004371939 = 0.76230044

The 95% confidence interval is [0.438, 0.762]

Interpretation: "I am 95% confident the interval from 0.438 to 0.762 contains the true value of the population proportion of people who call Heads when a fair coin is tossed."

Related Question Answer: Yes, because 0.50 falls within the interval limits, therefore, 50% is a plausible value for the proportion of all students who call Heads when a fair coin is tossed.