Problem 11.53

When 37 football helmets were subjected to an impact test, 25 sustained unacceptable damage.

1. Form a 90% confidence interval to estimate the population proportion.
2. Give an interpretation of this interval.
3. What sample size would be needed to carry out a second test, forming a 97% interval with a margin of error of 4%? (use the information from the previous sample)

Problem 11.54

J. Vuorinen carried out a series of experiments to gather information on the coefficient of permeability of concrete. In one experiment, the outflow of water from the pores of a concrete specimen after it had been under saturating water pressure for a period of time was recorded for different combinations of concrete permeability and porosity. The resulting water quantities after different lapses of time for one permeability-porosity combination are given in the table. (file: CONPERM1)

a. According to Vuorinen, "the quantity of water discharged is approximately in linear relationship with the square root of time" for most of the permeability-porosity combinations. Fit the following model to the data in the table:

Solution: First of all, we need to create a new variable to represent \(\sqrt{t}\) :

Now we use Minitab to run a regression analysis. The results are shown below:

This means that the regression equation is

b. Is there sufficient evidence to indicate that quality of water outflow and the square root of time are linearly related? Test using \[\alpha =.10\] .

Problem 11.55

Consider a normal population with the value of  known to be 1.32. A sample of size 34 resulted in a sample mean of 42.4. What is the confidence level for the interval (41.99, 42.81)?

Problem 11.56

The Journal of Applied Ecology published a study of the feeding habits of baby snow geese. The data on gosling weight change, digestion efficiency, acid-detergent fiber (all measured as percentages) and diet (plants or duck chow) for 42 feeding trials are saved in the SNOWGEESE file. Selected observations are shown in the following table. The botanists were interested in predicting weight change ( y ) as a function of the other variables. Consider the first-order model \[E(y)={{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+{{\beta }_{2}}{{x}_{2}}\] where \[{{x}_{1}}\] is digestion efficiency and \[{{x}_{2}}\] is acid-detergent fibre. (file: SNOWGEESE)

a. Find the least-squares prediction equation for weight change, y .

b. Interpret the \[\beta \] -estimates in the equation, part a .

c. Conduct a test to determine if digestion efficiency, \[{{x}_{1}}\] , is a useful linear predictor of weight change. Use \[\alpha =.01\] .

d. Form a 99% confidence interval for \[{{\beta }_{2}}\] . Interpret the result.

e. Find and interpret \[{{R}^{2}}\] and \[R_{a}^{2}\] . Which statistic is the preferred measure of model fit? Explain.

f. Is the overall model statistically useful for predicting weight change? Test using \[\alpha =.05\] .

Problem 11.63

The following data are the breaking loads for various types of fabrics that are unabraded and abraded.

1. Form a 95% confidence interval for the population mean difference in breaking load, assume a normal population.
2. According to the interval, is there a difference? Explain your answer.

Problem 11.64

Arsenic in groundwater. Refer to the Environmental Science & Technology study of the reliability of a commercial kit to test for arsenic in groundwater. From problem 11.20 recall that you fit a first-order model for arsenic level ( y ) as a function of latitude, longitude, and depth to the data saved in the ASWELLS file. Conduct a complete residual analysis of the model. Do you recommend any model modifications? (file: ASWELLS)

(Problem 11.20 as reference only for problem 11.64: A field kit was used to test a sample of 328 groundwater wells in Bangladesh. In addition to the arsenic level (micrograms per liter), the latitude (degrees), longitude (degrees), and depth (feet) of each well was measured.)

Problem 11.67

An aspirin manufacturer is purported to produce tablets with an average weight of 5 grains. A sample of 25 tablets results in an average weight of 4.87 grains with a standard deviation of .35 grains. Does this provide evidence to conclude that the tablets weigh less than 5 grains? Use =.05.

Problem 11.68

Create a multiple regression model that can be used to predict the suggested retail price for the vehicles in our 2004 car dataset. This model should use 2 or more x-variables (but not all the variables in our dataset) and should fit the assumptions for a multiple regression model fairly well. Show the equation for the final model and the ANOVA table for the model. Discuss what models were considered and why this model was chosen. (file: 04cars)

Problem 11.69

It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. This theory was tested by researchers who sent out a survey – some with a plain cover and the rest with a decorated cover. The researchers wanted to determine if there was a difference in the response rate. Of the 207 plain surveys, 104 were returned. Of the 213 decorated surveys, 109 were returned. Test the researchers’ hypothesis using 

Problem 11.71

The following table summarizes data on body weight gain both for a sample of animals given a dose of steroid and for a sample of control animals. According to prior studies the population variances can be considered the same.

1. Do the data suggest that the average weight gain for the control group exceeds that of the steroid group? Use a significance level of .05.
2. Test to see if the claim of equal variances is correct, using a significance level of .1.

Problem 11.73

A study on the symmetry of body parts found the following results comparing the sizes of right and left feet for the genders. Test to determine if these variables are related. Use 

Price: $37.5

Solution: The downloadable solution consists of 18 pages, 1950 words and 18 charts.
Deliverable: Word Document