students who participated in the​ study,

7878

correctly identified the color of the candy. The results are shown in the accompanying technology printout. Complete parts a through c below.

LOADING...

Click the icon to view the technology printout.

The proportion would be

0.50.5.

​(Type an integer or a​ decimal.)

b. Specify the null and alternative hypotheses for testing whether color and flavor are related. Choose the correct hypotheses below.

A.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p greater than 0.50H0: p=0.50 vs. Ha: p>0.50

B.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p less than 0.50H0: p=0.50 vs. Ha: p<0.50

C.

Upper H 0 : p not equals 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p≠0.50 vs. Ha: p=0.50

Your answer is not correct.

D.

Upper H 0 : p less than 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p<0.50 vs. Ha: p=0.50

E.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p not equals 0.50H0: p=0.50 vs. Ha: p≠0.50

This is the correct answer.

F.

Upper H 0 : p greater than 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p>0.50 vs. Ha: p=0.50

c.

Carry out the test and give the appropriate conclusion at

alphaαequals=0.010.01.

Use the​ p-value of the​ test, shown on the accompanying technology​ printout, to make your decision.

The​ p-value is

0.0020.002.

​(Type an integer or a​ decimal.)

Make the appropriate conclusion using

alphaαequals=0.010.01.

A.

RejectReject

the null​ hypothesis, because the​ p-value is

not less thannot less than

alphaα.

There is

insufficientinsufficient

evidence to conclude that color and flavor are related.

B.

Do not rejectDo not reject

the null​ hypothesis, because the​ p-value is not

not less thannot less than

alpha

Newton’s Law of Motion

Part 2 data: Tilted Track

(PLEASE SHOW ALL WORK)

1. Draw four FBD (free body diagrams) with Fnet vectors for the following four cases. (Neglect friction and drag.) (Define coordinate systems for each object, where each coordinate system is aligned with the object’s acceleration.)

a. Hanging mass while accelerating down (b). Cart on flat track while accelerating (from part 1 data)

c. Cart on inclined track while accelerating (d). Cart on declined track while accelerating (this is from part 2 data)

2. For case 1a above, write out Newton’s 2nd Law in the y-direction and solve for the tension: TH.

3. For cases 1b, 1c, and 1d, write out Newton’s 2nd Law in the x-direction and solve for the tension: TC.

4. Start an Excel data table and organize all your data (angles, mC, mH, and cart accelerations)

5. Nearby, start an Excel results table. Here, calculate the following quantities once per trial.

Reminder: If you use sine or cosine in MS Excel, it expects the angle to be entered in radians. You can input degrees by using “sin(radians(A1))” and “cos(radians(A1))”.    (Change “A1” to match your angle’s location.)

a. the net force acting on the cart, using Fnet=ma.

b. the net force acting on the hanging mass, using Fnet=ma.

c. the tension force, TH, acting on mH.

d. the tension force, TC, acting on mC. Do not use the tension value from part c!

e. the fraction TC/TH.     (What should this ratio be if your data was perfect?)

6. For your TC/TH values, calculate the average, standard deviation, and percent error between your average and the accepted value.

7. Make a single scatter plot showing the cart’s acceleration vs. the net force on the cart. Use three data series: 1) first four trials, 2) heavy cart, and 3) tilted track.

8. Add a linear trend line to each data set. For each trend line, use “Set Intercept” with a value of zero. Display the equation for each trend line.   (When the net force is zero, the acceleration had better be zero. Thus, the y-intercept should be 0 m/s2.)

The following experiment was carried out to evaluate a drug for the prevention of heart attacks. The subjects were 3,900 middle-aged men with heart trouble. Out of these men, 1,100 were assigned at random to receive the drug, and the remaining 2,800 were given a placebo. The subjects were followed for five years. In the group that received the drug, there were 220 deaths; in the control group, 2 there were 588 deaths. The 220 is 20% of the treatment group and the 588 is 21% of the control group. Someone argues as follows: “A one-percentage-point difference may not seem like much, but 1% of a million, for example, is 10,000. The drug will save tens of thousands of lives.” Do you agree or disagree with the statement? Explain and show mathematically.

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours. Language Spanish French German System 1 7 10 15 11 14 19 System 2 6 14 16 10 16 22 Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use . Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.

An experiment was conducted see the effect on fertilizer on production of Mameys. H0 : fertilizers have no impact on mamey production. H1 : fertilizers have an impact on mamey production. There are four treatment (a=4); three types of fertilizer and the control. Each treatment has four replicates (n=4). The number of mameys produced is given in the table below.

A. Using these data complete a 1-Way ANOVA table.

F1: 1, 2, 6, 11

F2: 2, 4, 2, 4

F3: 12, 4, 2, 6

Con: 3, 3, 1, 1

B. What is the proportion of explained variance for this treatment?

A psychologist conducted an experiment analysing the relationship between student scores in an exam and the amount of attention they paid in class. The latter was measured using a type of brain monitor. The Psychologist believed that scores would increase by 1 for every two unit increase in attention. The data are listed in the excel spreadsheet.

Estimate a linear regression between the score (Y) and the measure of attention(X).

(a) Write out the equation for Y in the form , but with coefficients. Show the estimated standard errors in parenthesis below the coefficients. What is the R2 of the regression? Calculate a 99 percent confidence interval for β.                                                               [5 pts]

(b) What are the mean and the estimated standard deviation of the estimated residuals? [2 pts]

Hint: the first answer is definitional and the second answer is easily seen from the output.

(c )Test the hypothesis that there is no relationship between the variables at the 90 percent significance level.                                                                                                    [3 pts]

(d) Test the hypothesis that the coefficient β=0.5 at the 99% significance level.               [3 pts]

(e) The Psychologist concluded from the experiment that test scores increase significantly if students pay attention in class. In one word, how would you describe the results of this experiment based on the data you have?                                                                                                       [2 pts]

DATA:

The following are some calculation questions related to the experiment. Please include the questions and their answers in your report:

a) A 0.05 L solution of 0.5 mol/L NaOH was titrated until neutralized into a 0.025 L sample of HCl. What was the concentration of the HCl?

b) 50 L of 2.0 mol/L Hydrochloric acid is titrated with sodium hydroxide to form water and sodium chloride. How many moles of sodium hydroxide are consumed in this reaction?

c) 100 L of 5 mol/L NaOH are required to fully titrate a 50 L solution of HCl. What is the initial concentration of the acid?

1. An experiment examined the impact of THC (the active ingredient in marijuana) on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Subjects came to the lab 3 times, each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC (a placebo). The order of the conditions was randomized in a double-blind design.

At the start of each session, no subject reported being “high.” After smoking the cigarette, participants rated how “high” they felt, using a positive continuous scale (0 representing not at all “high”). For the placebo condition, participants reported a mean “high” feeling of 11.3, with a standard deviation of 15.5. Is there evidence of a significant placebo effect, with subject feeling significantly “high” after smoking a placebo marijuana cigarette?

the appropriate null and alternative hypotheses for this study- H₀: m = 0 versus H_a: m > 0

a. What is the appropriate statistic to test this hypothesis? What is its value?

b. what is the P-value for the appropriate test? Specify the distribution used and all relevant parameters.

The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns, with a separate sample in each of the matrix cells. Demonstrate this with your own example, and describe what is meant by the main effects for each factor and the interaction between factors based on the numbers that you choose to plug in for each one of the cells.