1.The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 5.98 ounces and a standard deviation of 0.12 ounce. Suppose that you draw a random sample of 44 cans. Find the probability that the mean weight of the sample is less than 5.94 ounces.

Probability =

2.Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509and a standard deviation of 112.
(a)  If 1 man is randomly selected, find the probability that his score is at least 588.

(b)  If 18 men are randomly selected, find the probability that their mean score is at least 588.

Applicants to California community colleges are asked to indicate one of these education goals at the time of​ application: transfer to a​ four-year institution, an AA​ degree, a CTE​ certificate, job​ retraining, or personal enrichment. In a group of 500​ applications, describe a bar graph of these data that would have the least amount of variability. Also describe a bar graph that would have the most variability.

In a group of 500​ applications, describe a bar graph of these data that would have the least amount of variability. Choose the correct answer below.

A.

A bar graph with the least variability would be one where at least one of the options has no applications.

B.

A bar graph with the least variability would be one where each of the choices had a different number of applicants.

C.

A bar graph with the least variability would be one in which the applicants were equally divided among the five choices.

D.

A bar graph with the least variability would be one where most of the applicants had the same education​ goal, for example to transfer.

Describe a bar graph that would have the most variability. Choose the correct answer below.

A.

A bar graph with the most variability would be one in which the applicants were equally divided among the five choices.

B.

A bar graph with the most variability would be one where at least one of the options has no applications.

C.

A bar graph with the most variability would be one where each of the choices had a different number of applicants.

D.

A bar graph with the most variability would be one where most of the applicants had the same education​ goal, for example to transfer.

** Remember, there are examples in your notes at the end of each section**

The data set "cars" in R has 2 variables with 50 observations.
speed: numeric Speed (mph)
dist: numeric Stopping distance (ft)

Fill in the missing boxes below in the R code and then the corresponding predictor table from R.

Assume we want to test if dist a car travels can be determined by speed.

dat.lm = lm( __ ~ __ , data = __ )summary( __ )

a) Write the least squares line from the table above in the form ?̂= a + bx but filling the with the estimates of the coefficients.
?̂= __ + __x

b) Is there evidence to support that dist increases as the speed increases? Use ?=0.05.
1. ?₀ : ?₁ = 0 vs. ?? : ?₁> 0
2. ? = 0.05

3. t = __

4. Critical t_0.05,48 = t_0.05,40 = __

5. Conclusion:
Reject H0 OR Fail to reject H0

Interpretation:
There is sufficient evidence to support that dist increases as speed increases. OR
There is not sufficient evidence to support that dist increases as speed increases.

c) Find the 90% confidence interval for ?.

confint(dat.lm, 'speed', level = 0.90)

( __ , __ )

d) Find the 95% prediction interval for the mean when speed = 22.

newdat = data.frame( __ = __ )
predict( __ , __ , interval = 'prediction')

fit = __ , lwr = __ , upr = __

An article describes several studies of the failure rate of defibrillators used in the treatment of heart problems. In one study conducted by the Mayo Clinic, it was reported that failures were experienced within the first 2 years by 17 of 89 patients under 50 years old and 16 of 359 patients age 50 and older who received a particular type of defibrillator. Assume it is reasonable to regard these two samples as representative of patients in the two age groups who receive this type of defibrillator.

(a) Construct a 95% confidence interval for the proportion of patients under 50 years old who experience a failure within the first 2 years after receiving this type of defibrillator. (Round your answers to three decimal places.)
(  ,  )

Interpret the interval.

We are confident that the proportion of all patients under 50 years old who experience a failure within the first two years after receiving this type of defibrillator is within this interval at least 95% of the time.We are 95% confident that the proportion of all patients under 50 years old who experience a failure within the first two years after receiving this type of defibrillator is within this interval.    We are 95% confident that the proportion of all patients who experience a failure after receiving this type of defibrillator is within this interval.We are confident that 95% of all patients under 50 years old who experience a failure within the first two years after receiving this type of defibrillator are within this interval.

(b) Construct a 99% confidence interval for the proportion of patients age 50 and older who experience a failure within the first 2 years after receiving this type of defibrillator. (Round your answers to three decimal places.)
(  ,  )

Interpret the interval.

We are confident that 99% of all patients age 50 or older who experience a failure within the first two years after receiving this type of defibrillator is within this interval.We are confident that the proportion of all patients age 50 or older who experience a failure within the first two years after receiving this type of defibrillator is within this interval at least 99% of the time.    We are 99% confident that the proportion of all patients age 50 or older who experience a failure within the first two years after receiving this type of defibrillator is within this interval.We are 99% confident that the proportion of all patients who experience a failure after receiving this type of defibrillator is within this interval.

(c) Suppose that the researchers wanted to estimate the proportion of patients under 50 years old who experience a failure within the first 2 years after receiving this type of defibrillator to within 0.03 with 95% confidence. How large a sample should be used? Use the results of the study as a preliminary estimate of the population proportion. (Enter your answer as a whole number.)
patients

Consider a continuous random vector (Y, X) with joint probability density function

f(x, y) = 1                            for 0 < x < 1, x < y < x + 1.

1. What is the marginal density of X and Y? Use this to compute Var(X) and Var(Y)
2. Compute the expectation E[XY]
3. Use the previous results to compute the correlation Corr (Y, X)
4. Compute the third moment of Y, i.e., E[Y³]

This is a table summarizing the statistics between the number of words truthful people use vs people who are lying. To analyze this data;

• choose a t procedure, justify your choice, and perform it.
• Create a 95% confidence interval for (mean1 – mean2) and interpret this interval.
• Choose an appropriate hypothesis test and perform it (give hypothesis in words, symbols, test statistic, p-value, and conclusion)
• Interpret results.

The WT Company turns out 10,000 widgets a day. As everyone one knows, the most important part of a widget is the idge at its center. WT buys it idges from two other companies: Ser- tane Company can supply only 2,000 idges per day, but 99% of them work properly. The remaining 8,000 idges are purchased from Kwik Company; 10% of these are defective. Suppose a randomly domly chosen widget from WT has a defective idge. What is the probability that Kwik is responsible?

A cookie manufacturer is concerned about whether there is an unacceptably high degree of variability in the amount of chocolate chips that are in its most popular chocolate chip cookie. A sample of 15 cookies from the production line was collected so that a 99% confidence interval for the variance could be constructed. The sample variance was 16. Take all calculations toward the answer to three (3) decimal places, and report your answer to two (2) decimal places, without units.

The company can be 99% confident that the variance in the number of chocolate chips in the company's most popular cookie is between Blank 1 and Blank 2 .

Find the confidence interval specified. Assume that the population is normally distributed.

The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
8.3 7.3 13.8 12.6 11.1
9.5 13.7 14.2 9.8 12.6

Determine a 95% confidence interval for the mean time for all players

12.90 to 9.70 min

9.70 to 12.90 min

13.00 to 9.60

9.60 to 13.00 min

There is some evidence that high school students justify cheating in class on the basis of poor teacher skills. Poor teachers are thought not to know or care whether students cheat, so cheating in their classes is OK. Good teachers, on the other hand, do care and are alert to cheating, so students tend not to cheat in their classes. A researcher selects three teachers that vary in their teaching performance (Poor, Average, and Good). 6 students are selected from the classes of each of these teachers and are asked to rate the acceptability of cheating in class.

How acceptable is cheating in class?

Extremely Very Somewhat Neutral Somewhat Very Extremely unacceptable unacceptable unacceptable acceptable acceptable   acceptable 1 2 3 4 5 6 7

a. Use SPSS to conduct a One-Way ANOVA with α= 0.05 to determine if teacher quality has a significant effect on cheating acceptability. State your hypotheses, report all relevant statistics, include the ANOVA table from SPSS, and state your conclusion.

b. Use SPSS to conduct post hoc testing. To run a post hoc test in SPSS, open the One-Way ANOVA window (used above) and click the “Post Hoc” button. Check the boxes next to LSD and Bonferroni.

State the results of the post hoc tests (which means are significantly different from each other) and include SPSS printouts as part of your answer to this question.

Use SPSS to determine if academic program is related to feelings about PSYC 3002 by computing the appropriate chi square test.

1. Recall the four scales of measurement you learned about in Week 1 (i.e., nominal, ordinal, interval, ratio). Explain what scale of measurement is used to measure academic program in this example. How do you know?

2. Explain what scale of measurement is used to measure feeling about PSYC 3002. Explain how you know.

3. State whether this scenario requires a goodness of fit test or a test of independence. Explain your answer.

4. Before computing the chi square, state the null hypothesis and alternative hypothesis in words (not formulas).

5. Identify the obtained χ2 using SPSS and report it in your answer document.

6. State the degrees of freedom and explain how you calculated it by hand.

7. Identify the p value using SPSS and report it in your answer document.

8. Explain whether you should retain or reject the null hypothesis and why.

9. Are the results statistically significant? How do you know?

10. Explain what you can determine about the relationship between academic program and feelings about PSYC 3002.

DATA SET:

1. In 1994, baseball management and the players union failed to come to an agreement and the management initiated a work stoppage. The two sides did not come to an agreement until 1995. As a result less baseball games were played in both the 1994 and 1995 season. The 1994 and 1995 data seem to be outside the pattern of the rest of the data. Determine if these two data points are influential by:

a) Plot the regression line from the full data set on the on the scatter plot. The regression equation is: Wins = 24.5 + 0.08Runs, mark it “ALL SEASONS”

b) ​​​​​​​Plot the regression line from data set without the partial seasons on the on the scatter plot. The regression equation is: Wins = 43.3 + 0.05RUNS, mark it “ONLY FULL SEASON”. Do the partial seasons seem to be influential? Explain.

c) Using the linear regression model for “ALL GAMES” in the Red Socks data, Wins = 24.5+ 0.08 Runs. Consider the data for the year 2004, (Runs = 949, Wins = 98) Calculate the residual for this year.

d) The coefficient of determination = 67.2% for the Red Socks data. Find the linear correlation coefficient. Round your answer to 2 decimal places.

(Solving with excel workbook)

A large corporation must reserve a hotel room block for its annual stockholders' meeting. Based on history, the number of attendees will be normally distributed with mean 4900 and standard deviation 1000. Rooms can be reserved now for a cost of $150/room. If the number of rooms reserved is less than attendance, additional rooms must be reserved at a cost of $250/room. If the number of rooms reserved is greater than attendance, the corporation must indemnify the hotel at the rate of $75 per unused room.

The boss tells you: "I am going to reserve 4300, 4400, 4500, 4600, 4700, 4800, 4900, 5000, 5100, or 5200 rooms, whichever you recommend. Please give me your recommendation." (first number requested)

Redo the problem: The number attending has a triangular distribution with minimum 2000, most likely value 4900, and maximum value 6900. Again, he boss tells you: "I am going to reserve 4300, 4400, 4500, 4600, 4700, 4800, 4900, 5000, 5100, or 5200 rooms, whichever you recommend. Please give me your recommendation." (second number requested)

For the first part of the problem, what is the chance that the random number sampled from the normal is negative, to 3 significant decimal digits? (third number requested)

The commercial division of a real estate firm is conducting a regression analysis of the relationship between , annual gross rents (in thousands of dollars), and , selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.

a. How many apartment buildings were in the sample?

b. Write the estimated regression equation (to 2 decimals if necessary).

c. Use the  statistic to test the significance of the relationship at a  level of significance.

What is the -value? Use Table 1 of Appendix B.

-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 4

What is your conclusion?

- Select your answer -Cannot conclude that the selling price is related to annual gross rents. OR Conclude that the selling price is related to annual gross rents.Item 5

d. Use the F statistic to test the significance of the relationship at a  level of significance.

Compute the F test statistic (to 2 decimals).

What is the -value?

-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 7

What is your conclusion?

- Select your answer -Cannot conclude that the selling price is related to annual gross rents. or Conclude that the selling price is related to annual gross rents.Item 8

e. Predict the selling price of an apartment building with gross annual rents of  (to 1 decimal).

  thousands.

Show that the following functions are probability density functions for some value of k and determine k. Then, determine the mean ((a),(c),(e),(g)) and variance ((b),(d),(f),(h)) of X. Round your answers to three decimal places (e.g. 98.765).

(a),(b)f (x) = kx2 for 0 < x < 8

(c),(d)f (x) = k(1 + 2x) for 0 < x < 22

(e),(f)f (x) = ke-x for 0 < x

(g),(h)f (x) = k where k > 0 and 101 < x < 101 + k