The following data is representative of that reported in an article on nitrogen emissions, with x = burner area liberation rate (MBtu/hr-ft²) and y = NO_x emission rate (ppm):

(a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Round all numerical values to four decimal places.)
y =

(b) What is the estimate of expected NO_x emission rate when burner area liberation rate equals 240? (Round your answer to two decimal places.)
ppm

(c) Estimate the amount by which you expect NO_x emission rate to change when burner area liberation rate is decreased by 50. (Round your answer to two decimal places.)
ppm

(d) Would you use the estimated regression line to predict emission rate for a liberation rate of 500? Why or why not?

Yes, the data is perfectly linear, thus lending to accurate predictions. Yes, this value is between two existing values.     No, this value is too far away from the known values for useful extrapolation. No, the data near this point deviates from the overall regression model.

An article gave a scatter plot along with the least squares line of x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. The accompanying values were read from the plot.

(a) Does a scatter plot of the data support the use of the simple linear regression model?

Yes, the scatterplot shows a reasonable linear relationship. Yes, the scatterplot shows a random scattering with no pattern.     No, the scatterplot shows a reasonable linear relationship. No, the scatterplot shows a random scattering with no pattern.

(b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to five decimal places.)

(c) Calculate a point estimate of the true average runoff volume when rainfall volume is 47. (Round your answer to four decimal places.)
m³

(d) Calculate a point estimate of the standard deviation σ. (Round your answer to two decimal places.)
m³

(e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)

Forma a 95% confidence interval on the mean pouring temperature for iron castings if a sample of size 25 yielded a mean of 2560 and a standard deviation (s) of 20.

An article gave a scatter plot along with the least squares line of x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. The accompanying values were read from the plot.

(a) Does a scatter plot of the data support the use of the simple linear regression model?

Yes, the scatterplot shows a reasonable linear relationship. Yes, the scatterplot shows a random scattering with no pattern.     No, the scatterplot shows a reasonable linear relationship. No, the scatterplot shows a random scattering with no pattern.

(b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to five decimal places.)

(c) Calculate a point estimate of the true average runoff volume when rainfall volume is 47. (Round your answer to four decimal places.)
m³

(d) Calculate a point estimate of the standard deviation σ. (Round your answer to two decimal places.)
m³

(e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)

For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data:

(a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)
y =

Interpret the slope.

A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.     A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope.

(b) Calculate the coefficient of determination. (Round your answer to four decimal places.)


Interpret the coefficient of determination.

The coefficient of determination is the number of the observed samples of axial strength of asphalt that cannot be explained by variation in cube strength. The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that cannot be attributed to its linear relationship with cube strength.     The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that can be attributed to its linear relationship with cube strength. The coefficient of determination is the number of the observed samples of axial strength of asphalt that can be explained by variation in cube strength.

(c) Calculate an estimate of the error standard deviation σ in the simple linear regression model. (Round your answer to three decimal places.)
MPa

Interpret the estimate of the error standard deviation σ in the simple linear regression model.

The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount greater than one error standard deviation. The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within one error standard deviation.     The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within two error standard deviations. The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount greater than two error standard deviations.

Suppose a survey of 500 people age 18 to 34 indicated that 32.2% of them live

with one or both of their parents. Calculate and interpret a confidence interval estimate for the true proportion

of all people age 18 to 34 who live with one or both parents. Use a 94% confidence level.

Suppose the mean income of firms in the industry for a year is 25 million dollars with a standard deviation of 9 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 34 million dollars? Round your answer to four decimal places.

Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is what? For each pairwise comparison.

(c)Which of the comparisons had significant differences? (Select all that apply.)

The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference.

Recall following no delay was significantly different from recall following a half second delay.

Recall following a half second delay was significantly different from recall following a one second delay.

Recall following no delay was significantly different from recall following a one second delay.

You may need to use the appropriate table in Appendix B to answer this question.

An educational psychologist wants to see the impact of mnemonics on memory. To test this the psychologist designs a study where participants are randomly assigned to a mnemonic method or not. However, before the participants are assigned they are paired for vocabulary knowledge. All the participants are then asked to read a passage from a book. A few days later, the participants are asked to reproduce the passage. Below are the number of correctly recalled words when reproducing the passage. What can the psychologist conclude with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na OR z-test OR One-Sample t-test OR Independent-Samples t-test OR Related-Samples t-test

b)
Condition 1:
---Select--- the book OR correctly recalled words OR control OR the passage OR mnemonic
Condition 2:
---Select--- the book OR correctly recalled words OR control OR the passage OR mnemonic

c) Input the appropriate value(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value = _____ ; Decision:  ---Select--- Reject H0 OR Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d = _____ ;   ---Select--- na OR trivial effect OR small effect OR medium effect OR large effect
r² = _____ ;   ---Select--- na OR trivial effect OR small effect OR medium effect OR large effect

e) Make an interpretation based on the results.

A) Participants learning the mnemonic method significantly recalled more correct words than those in the control.

B) Participants learning the mnemonic method significantly recalled less correct words than those in the control.   

C) There was no significant difference in correctly recalling words between the mnemonic method and the control.

Some studies show that people who think they are intoxicated will show signs of intoxication, even if they did not consume alcohol. To test whether this is true, researchers had a group of five adults consume nonalcoholic drinks, which they were told contained alcohol. The participants completed a standard driving test before drinking and then after one nonalcoholic drink and after five nonalcoholic drinks. A standard driving test was conducted in a school parking lot where the participants had to maneuver through traffic cones. The number of cones knocked over during each test was recorded. The following table lists the data for this hypothetical study.

(a) Complete the F-table. (Round your answers to two decimal places.)

(b) Compute a Bonferroni procedure and interpret the results. (Assume experimentwise alpha equal to 0.05. Select all that apply.)

Students knocked over significantly more cones after 1 nonalcoholic drink compared with the driving test prior to drinking.

Students knocked over significantly more cones after 5 nonalcoholic drinks compared with the driving test prior to drinking.

Students knocked over significantly more cones after 5 nonalcoholic drinks compared with the driving test after 1 nonalcoholic drink.

There were no significant differences between any of the groups.

Administrators want to know if test anxiety is impacted by the number of college years completed. After completing their freshman year, a random sample of students was selected and given the College Test Anxiety Questionnaire (CTAQ); higher scores indicate more test anxiety. After completing their junior year they were again tested. What can the administrators conclude with α = 0.05?

a) What is the appropriate test statistic?
---Select--- na OR z-test OR One-Sample t-test OR Independent-Samples t-test OR Related-Samples t-test

b)
Condition 1:
---Select--- junior OR CTAQ OR test anxiety OR number of college years OR freshman
Condition 2:
---Select---junior OR CTAQ OR test anxiety OR number of college years OR freshman

c) Input the appropriate value(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value = _____ ; Decision:  ---Select--- Reject H0 OR Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d = _____ ;   ---Select--- na OR trivial effect OR small effect OR medium effect OR large effect
r² = _____ ;   ---Select--- na OR trivial effect OR small effect OR medium effect OR large effect

e) Make an interpretation based on the results.

A) Students showed significantly less anxiety in their junior year as opposed to their freshman year.

B) Students showed significantly more anxiety in their junior year as opposed to their freshman year.    

C) Students showed no significant anxiety difference between their junior and freshman year.

Suppose x has a distribution with μ = 30 and σ = 23.

(a) If a random sample of size n = 42 is drawn, find μ_x, σ_x and P(30 ≤ x ≤ 32). (Round σ_x to two decimal places and the probability to four decimal places.)

(b) If a random sample of size n = 70 is drawn, find μ_x, σ_x and P(30 ≤ x ≤ 32). (Round σ_x to two decimal places and the probability to four decimal places.)

If n = 320 and ˆ p (p-hat) = 0.15, construct a 99% confidence interval.

Give your answer to three decimals __<P<___

Binomial distribution. Tables must be completed in excel only.

1. A report to Health Canada indicated that an intensive education program was used in an attempt to lower the rate of lung cancer development among females. After running the program, a long-term follow-up study of 505 females was conducted, which revealed the current rate of lung cancer development is 7.5 %.

1. Find the probability that 10 or less females have lung cancer development.
2. Assuming the program has effect, find the mean and standard deviation for the number of lung cancer cases in groups of 505 females.      
3. Considering that unusual values are outside the interval μ-2σ, μ+2σ, is 20 females out of 505 females with lung cancer development unusually low or not? Show calculations.   

A company operates three machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.

• A. Yes, you can reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.0423
• B. Yes, you can reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.9577
• C. No, you cannot reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.0423
• D. No, you cannot reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.9577