Given the following data that was sampled from a normal population distribution: 1257 1306 1250 1292 1268 1316 1275 1317 1275

Determine a 95% confidence interval for the population mean. (round to nearest integer)

lower limit

upper limit

A table of house pricing data is linked below. Use software to do further analyses with the multiple regression model of y=selling price of home in​ thousands, x1=size of​ home, and x2=number of bedrooms. Then use this model to complete parts a through c below.

Data:

y_Price_($)   x1_Size_(sq_ft)   x2_Bedrooms
309900   3179   5
161700   1738   3
162100   1901   2
132100   996   1
210900   1676   2
170100   1662   2
189700   1396   2
286100   3627   4
304700   3961   5
252700   3395   5
120200   795   1
286600   3475   4
167800   1416   2
118200   1041   1
260900   2763   4

b. Report and interpret the t statistic and​ P-value for testing H_0​: β₂ = 0 against H_a​: β₂ > 0.

t = 1.093

c. Report the p-value corresponding to this t statistic.

P-value = ____ (round to four decimal places as needed)

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 590⁢HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 580 with a standard deviation of 45⁢HP. Assume the population is normally distributed.

Step 1 of 2 :  

Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.01. Round your answers to two decimal places.

1. For each of the 2 majors, conduct a full hypothesis test at the 10% significance level:
   • The mean ‘Cost’ for a college is $160,000.
2. 2. For Business versus Engineering majors conduct a full, two-sample, full hypothesis test at the 5% significance level (assume the variances are not equal):The average ’30-Year ROI’ for Business majors is less than for Engineering Majors.

1. 3.  In a highlighted box, explain how each hypothesis test contributes to the central question of which major would give the better ROI. Why do we need hypothesis testing? Isn't it enough to look at the sample of 20 schools and look at those numbers? What exactly does hypothesis testing do that looking at the numbers in the sample and saying "one is higher than the other" cannot do? This answer is critical to your final project. It demonstrates that you understand why you just can't look at the mean, median, and mode of the spreadsheet and "call it a day."

   Business				Engineering
   Private	$222,700.00	$1,786,000.00	7.70%	Private	$221,700.00	$2,412,000.00	8.70%
   Private	$176,400.00	$1,758,000.00	8.40%	Private	$213,000.00	$2,064,000.00	8.30%
   Private	$212,200.00	$1,714,000.00	7.80%	Private	$230,100.00	$1,949,000.00	7.90%
   Public	$125,100.00	$1,535,000.00	9.10%	Private	$222,600.00	$1,947,000.00	8.00%
   Private	$212,700.00	$1,529,000.00	7.40%	Private	$225,800.00	$1,938,000.00	8.00%
   Public	$92,910.00	$1,501,000.00	10.10%	Public	$87,660.00	$1,937,000.00	11.20%
   Private	$214,900.00	$1,485,000.00	7.30%	Private	$224,900.00	$1,915,000.00	7.90%
   Private	$217,800.00	$1,483,000.00	7.20%	Private	$221,600.00	$1,878,000.00	7.90%
   Private	$225,600.00	$1,444,000.00	7.00%	Public	$125,100.00	$1,854,000.00	9.80%
   Private	$217,300.00	$1,442,000.00	7.10%	Private	$215,700.00	$1,794,000.00	7.90%
   Private	$226,500.00	$1,441,000.00	7.00%	Public	$92,530.00	$1,761,000.00	10.60%
   Private	$215,500.00	$1,438,000.00	7.20%	Private	$217,800.00	$1,752,000.00	7.70%
   Private	$223,500.00	$1,428,000.00	7.00%	Public	$89,700.00	$1,727,000.00	10.70%
   Private	$226,600.00	$1,414,000.00	7.00%	Private	$229,600.00	$1,716,000.00	7.50%
   Private	$189,300.00	$1,397,000.00	7.50%	Public	$101,500.00	$1,703,000.00	10.20%
   Public	$89,700.00	$1,382,000.00	9.90%	Public	$115,500.00	$1,694,000.00	9.70%
   Public	$87,030.00	$1,376,000.00	10.00%	Public	$104,500.00	$1,690,000.00	10.10%
   Private	$218,200.00	$1,343,000.00	6.90%	Public	$69,980.00	$1,685,000.00	11.50%
   Private	$229,900.00	$1,339,000.00	6.70%	Private	$219,400.00	$1,676,000.00	7.60%
   Private	$148,800.00	$1,321,000.00	8.10%	Public	$64,930.00	$1,668,000.00	11.70%

Consider a manufacturing line with 3 robotic machines used to create a widget. Each robotic machine either performs (P) perfectly or creates a (D) defect. Denote the outcome of the widget by creating 3-tuples of P's and D's.

1) Find the sample space S.

2) Find the event A that at least one robotic machine created a defect (D).

3) Find event B that all three robotic machines performed the same way.

4) Are the events A and B mutually exclusive? Show mathematically using set theory notation.

Identify the critical t. An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t value ?∗t∗ for the given sample size and confidence level. Round critical t values to 4 decimal places.

1. What is the equation for the regression line? What does each term refer to?
2. What assumptions are required to calculate the various inferential statistics of linear regression?

Consider the following contingency table of observed frequencies. Complete parts a. through d. below.

Click the icon to view the contingency table.

Column Variable

Row Variable    C1 C2    C3

R1 11    9 12

R2 11    6 6

a. Identify the null and alternative hypotheses for a​ chi-square test of independence with based on the information in the table. This test will have a significance level of alpha α=0.01. Choose the correct answer below.

A. H0​: The row and column variables are not independent of one another. H1​: The row and column variables are independent of one another.

B. H0​: The variables R1​, R2​, C1​, C2​, and UpperC3 are independent. H1​: At least one of the variables is not independent.

C. H0​: The variables R1​, R2​, C1​, C2​, and C3 are independent. H1​: None of the variables are independent.

D. H0​: The row and column variables are independent of one another. H1​: The row and column variables are not independent of one another. ​

b, Calculate the expected frequencies for each cell in the contingency table.

Column Variable

Row Variable    C1 C2    C3

R1

R2

​(Round to two decimal places as​ needed.)

c. Calculate the​ chi-square test statistic.

χ2=(Round to two decimal places as​ needed.)

d. Determine the​ p-value. Using alpha α=0.01​, state your conclusions. ​

p-value= ​(Round to three decimal places as​ needed.) State your conclusions.

The​ p-value is (greater than/less than) alpha α= 0.01​, so (reject/do not reject) H0. There is (sufficient/insufficient) evidence to indicate that (the row and column variables are not independent of one another//at least one of the variables is not independent//the row and column variables are independent of one another. /none of the variables are independent/ the variables R1, R1, C1, C2, and C3 are independent. (pick one) Click to select your answer(s).

1. Every Normal model is defined by its parameters, the mean and the standard deviation. For each model described here, find the missing parameter. As always, start by drawing a picture.

   1. μ=20, 45% above 30, σ= ?

   2. μ=88, 2% below 50, σ= ?

   3. σ=5, 80% below 100, μ=?

   4. σ=15.6, 10% above 17.2, μ=?

a.) The shelf life of Energized AA batteries is normally distributed, with a mean of 10 years and a standard deviation of 0.1 years. What is the value of the shelf life for the first quartile?

b.) The time it takes Professor Smith the grade a single midterm exam is normally distributed with a mean of 5 minutes and a standard deviation of 1.7 minutes. If there are 60 students in her class, what is the probability it will take her longer than 5 hours to grade all of the midterm exams?

1. The best measure for model selection is the Adjusted R-square.
2. Partial sums of squares are more useful than sequential sums of squares.
3. If we have a categorical variable with 4 categories we will need 4 dummy variables to model this.

Do the poor spend the same amount of time in the shower as the rich? The results of a survey asking poor and rich people how many minutes they spend in the shower are shown below. Poor 13 9 35 20 30 26 30 10 12 20 18 Rich: 37 15 22 37 26 48 45 43 47 19 47 20 Assume both follow a Normal distribution. What can be concluded at the the α = 0.05 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H0: (please enter a decimal) H1: (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is not the same as the population mean time in the shower for the rich. The results are statistically significant at α = 0.05, so there is sufficient evidence to conclude that the mean time in the shower for the eleven poor people that were surveyed is not the same as the mean time in the shower for the twelve rich people that were surveyed. The results are statistically insignificant at α = 0.05, so there is insufficient evidence to conclude that the population mean time in the shower for the poor is not the same as the population mean time in the shower for the rich. The results are statistically insignificant at α = 0.05, so there is statistically significant evidence to conclude that the population mean time in the shower for the poor is equal to the population mean time in the shower for the rich.

1. 5. Scenario: A survey is conducted to determine the average number of people living in a household in Scranton. An interviewer asks a sample of 16 Scranton shoppers, selected randomly in the Viewmont Mall (no two living in the same household), how many people live in their household. The results are as follows: 1        1      1      2     2     2      2     2   2     3     3     3     4     4    5     6

Assume the distribution of the number in all households is approximately normal. Do each of the following:

1. Determine the mean and standard deviation for the sample data from the survey.

x̄ = ______________                                    s = __________________

2. Using the sample results in Part (a), find a 95% confidence interval for the mean number of members in all Scranton households.

                We can be _____________________________________________________________________

(c ) Given that the census bureau finds the standard deviation of all households sizes in Scranton is 1.28, find the number of sample items required for a 99% confidence level for the mean of the population to be accurate within a margin of error of 0.1.

n = _______________

Gru's schemes have a/an 11% chance of succeeding. An agent of the Anti-Villain League obtains access to a simple random sample of 1100 of Gru's upcoming schemes.
Find the probability that...
(Answers should be to four places after the decimal, using chart method, do NOT use the continuity correction):

...less than 101 schemes will succeed:

...more than 95 schemes will succeed:

...between 95 and 101 schemes will succeed:

...less than 8.5% of schemes will succeed:

...more than 9.5% of schemes will succeed:

...between 8.5% and 9.5% of schemes will succeed:

Does delaying oral practice hinder learning a foreign language? Researchers randomly assigned 23 beginning students of Russian to begin speaking practice immediately and another 23 to delay speaking for 4 weeks. At the end of the semester both groups took a standard test of comprehension of spoken Russian. Suppose that in the population of all beginning students, the test scores for early speaking vary according to the N(29, 6) distribution and scores for delayed speaking have the N(28, 3) distribution.
(a) What is the sampling distribution of the mean score x in the early speaking group in many repetitions of the experiment? (Round your answers for s to two decimal places.)
Mean   =
1.3

Incorrect: Your answer is incorrect.
s   =

What is the sampling distribution of the mean score y in the delayed speaking group?
Mean   =
s   =

(b) If the experiment were repeated many times, what would be the sampling distribution of the difference y - x between the mean scores in the two groups? (Round your answer for s to two decimal places.)
Mean   =
s   =

(c) What is the probability that the experiment will find (misleadingly) that the mean score for delayed speaking is at least as large as that for early speaking? (Round your answer to four decimal places.)