10.2.6: Tech Lab 6
- Page ID
- 63697
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Tech Lab 6 - Interval Estimates
Purpose
In this technology lab we learn how to use Excel to help us find critical values and construct confidence intervals for proportions and means.
Confidence Intervals
You have all the equations needed to construct any type of confidence interval (interval estimate) in the text, but calculating these has a lot of steps. Excel can help!
Open the Interval_Estimates_Blanks Excel file and save it with a new file name. Use the interval estimate questions (with answers) below as test problems to enter in and be sure your template is working out the calculations correctly.
You can see the proportions interval estimate template filled out in this video: Interval Estimates template example (11:00)
Confidence Interval Test Problems
Proportion
Of 101 randomly selected adults, 35 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure. Is this a large proportion?
[Answer: 
, this is quite a big range, from about a quarter to nearly half, but it does seem like a pretty big proportion of people have high blood pressure]
Mean, sigma unknown
A principal randomly selected six students to take an aptitude test. Their scores had mean 80.6 and standard deviation 6.23. If we assume the test scores on the aptitude test are normally distributed, determine a 96% confidence interval for the mean score for all students.
[Answer: 
]
Mean, sigma known
This tab is optional as we won’t really use it since it’s rare to have a population standard deviation. It might be good practice to fill it in though, up to you.
37 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 17.0 lbs and all packages from similar parcel services typically have a standard deviation of 3.3 lbs. What is the 90% confidence interval for the true mean weight of all packages received by the parcel service?
[Answer: 
]
Sample Size Proportion
Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 95% confident that the population proportion is estimated to within 0.03? If we knew that the proportion was approximately 90%, what would the minimum sample size be?
[Answers: In the first case, 
. In the second case 
]
Sample Size Mean
The average height of young adult males has a normal distribution with standard deviation of 2.5 inches. You want to estimate the mean height of male students at your college or university to within one inch with 93% confidence. How many male students must you measure?
[Answer: 
]
Two Means from Independent Samples
Suppose you want to estimate the difference in weight between two different species of turtles. You take a random sample from each species and weight the turtles. In the first sample of 15 turtles, the mean weight was 310 lbs with standard deviation 18.5 lbs. The second sample (from the other species) of 15 turtles, the mean weight was 300 lbs with standard deviation 16.4 lbs. Find a 92% confidence interval for the difference in the mean weight of the two species. Do their weights seem to differ significantly?
[Answer: -1.61214509 < 
< 21.61214509, While the first species did have a higher sample mean weight, the two means are pretty close together and the interval estimate for their difference contains 0, meaning that it’s possible there’s no difference at all in the population mean weights. It seems likely that the two populations have the same or close to the same mean weights.]
Two Proportions
A medical researcher conjectures that smoking can result in the wrinkled skin around the eyes. The researcher recruited 150 smokers and 250 nonsmokers to take part in an observational study and found that 95 of the smokers and 105 of the nonsmokers were seen to have prominent wrinkles around the eyes (based on a standardized wrinkle score administered by a person who did not know if the subject smoked or not). Find a 95% confidence interval for the difference in the proportion of smokers with wrinkles and the proportion of non-smokers with wrinkles. Does there seem to be a significant difference between the rates of wrinkles from the two groups?
[Answer: 0.114894 < 
< 0.311772, yes, it does seem that smokers are more likely to have eye wrinkles]