The Ablex political party claims that more than 50% of Bloornians prefer their party to the Xyblex party. Perform a hypothesis test to the test the claim with alfa= 0.05 using a sample of 35 Bloornians a) Write the claim symbolically for this scenario b) Write the Hypothesis for this scenario Ho and HA c) Give the value of the Test Statistic, including whether it is a a t- or z- statistic. If applicable, also give d.f d) Indicate which method you are using: Critical value or P-Value. Give the values obtained or the P-value e) What is your conclusion. Reject Ho, accept Ho, Fail to Reject Ho or Fail to accept Ho f) If 55% of the population actually prefer the Ablex party, which (if any) error has been made. No error, type I error, Type II error or Critical Error Sample is 35 Bloornians (or persons) and 20 of them preferred the Ablex political party.

A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 14 of the plates have blistered.

z = 1.33

p- value = 0.0913

(b) If it is really the case that 16% of all plates blister under these circumstances and a sample size 100 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the 0.05 test? (Round your answer to four decimal places.)

If it is really the case that 16% of all plates blister under these circumstances and a sample size 200 is used, how likely is it that the null hypothesis of part (a) will not be rejected by the 0.05 test? (Round your answer to four decimal places.)

(c) How many plates would have to be tested to have β(0.16) = 0.10 for the test of part (a)? (Round your answer up to the next whole number.)

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.

(a) Verify that

Σx = 480,

Σy = 86.7,

Σx² = 63,482,

Σy² = 2025.67,

Σxy = 11174.1,

and

r ≈ 0.94564.

(b) Use a 1% level of significance to test the claim

ρ > 0.

(Use 2 decimal places.)

Conclusion

(c) Verify that

S_e ≈ 4.2911,

a ≈ 1.6127,

and

b ≈ 0.1638.

(d) Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2 decimal places.)

= km/100

(e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)

(f) Use a 1% level of significance to test the claim that

β > 0.

(Use 2 decimal places.)

(g) Find a 95% confidence interval for β and interpret its meaning in terms of drift rate. (Use 2 decimal places.)

Lower limit=

Upper limit=

(h) Consider the following scenario. A sailboat had an accident and radioed a Mayday alert with a given latitude and longitude just before it sank. The survivors are in a small (but well provisioned) life raft drifting in the part of the Pacific Ocean under study. After 30 days, how far from the accident site should a rescue plane expect to look? (Use 2 decimal places.)
= km/100

Why can't correlations tell us anything about cause and effect?  Going further, what kind of an experimental design would you need to explain cause and effect?  Provide an example to illustrate your point.

It is well established that both nature (genetics) and nurture (environment) play a role in who we are and how we behave as humans. One way to examine the effect of nature vs. nurture is to study children who have been adopted at birth. These children are unique in that they received genes from their birth parents and have environmental influence from their adoptive parents. For example, a research study can be conducted to see if the Body Mass Index (BMI) is more correlated with the BMI of his/her birth parent or adoptive parent. If the BMI of the child is more correlated with the birth parent’s BMI, it means that the weight might be genetically determined to a larger extent compared to environmental influence. If it’s more correlated with the adoptive parent’s BMI, then it means that the weight might be influenced by the behavior of the adoptive parent to a larger extent.

Use the following dataset to answer the questions below:

Questions:

1. Calculate the mean and standard deviation for the adoptive parents’ BMI. (2 points total: 1 for mean and 1 for SD- deduct .5 if the process is correct but result is wrong)

2. Calculate the Z scores for all the data points for the adoptive parents. (1 point for calculating adoptive parents’ Z scores. Deduct .5 for each error in calculation)

3. Calculate the Pearson’s correlation coefficient r between children’s BMI and their adoptive parents’ BMI. Note that the children’s Z scores have been calculated in Part 1 of this scenario. (2 points total: 1 for work, 1 for r value)

4. Explain the direction and strength of the relationship based on the r. (2 points total: 1 for direction, 1 for strength)

5. What is the proportion of shared variance between children’s BMI and their adoptive parents’ BMI? That is, how much of the variance in the children’s BMI can be predicted from their adoptive parents’ BMI? (2 points total: 1 for work, 1 for result)

6. Based on the two r statistics, what would be the answer to the research question of whether children’s BMI is influenced more by nature or nurture? (1 point)

*****Show step-by-step in Excel******

An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year ( X1 ) and the age of the car ( X2 , in years) at the beginning of the year. The company has gathered the data on 10 automobiles and the regression information from Excel is presented below. Use this information to answer the following questions.

Summary measures Multiple R 0.9689 R-Square 0.9387 Adj R-Squared 0.9212 StErr of Estimate 72.218

a. Use the information above to write out the estimated linear regression model.

b. Interpret each of the estimated coefficients of the regression model in part (a).

c. Identify and interpret the coefficient of determination ( R2 ) and the adjusted R2 .

d. Does the given set of explanatory variables do a good job of explaining changes in the maintenance costs? Explain why or why not.

In this exercise you are choosing between the following investment strategies:

Invest $200 in stock A. Stock A costs $20 per share. Expected yield per share of stock A is $2, and the variance of yield per share is 9 ($-squared).

Invest $200 in stock B. Stock B costs $10 per share. Expected yield per share of stock B is $0.90, and the variance of yield per share is 1 ($-squared).

Invest $100 in stock A and $100 in stock B. The correlation between yield per share of stock A and yield per share of stock B is 0.12.

1)With strategy (iii), how many shares of stock A and stock B do you buy?

a) 10 shares of A and 20 shares of B

b) 5 shares of A and 10 shares of B

c)10 of each

d) 20 of each

2)What is the value of the covariance between the yield on a share of stock A and the yield on a share of stock B?

a) 0.16

b)0.12

c) 1.08

d) 0.36

3) When will portfolio (iii) lose money?

a) When the yield on portfolio (iii) is less than the expected yield on portfolio (iii)

b) When the yield on portfolio (iii) is negative

c) When the yield on stock A is negative and the yield on stock B is negative

d)When the yield on stock A is negative or the yield on stock B is negative

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 28 houses that sold in their neighborhood took an average time of 220 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 40 days. [You may find it useful to reference the z table.]

b. Construct the 95% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 10 years was approximatley normal with mean of 95 days and a standard deviation of 29 days. The property management company intends to update the kitchen appliances in the apartments that were empty for top 10% of durations. What is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances? Round to the nearest whole number.
Choose 1 answer:
A) 48 days
B) 112 days
C) 114 days
D) 123 days
E) 129 days

This is a two part question:

a) How will the company benefit from implementing Design for Reliability (DFR)

program? Names four of such benefits.

b) What are some of the critical inputs to Design FMEA/FMECA? Please name four

and very briefly discuss.

1. You are a nursing researcher and you are interested in whether university grades are predictive of performance on the NCLEX exam. You randomly select a sample of 25 nurses from the Ontario registry and obtain each nurse’s score on the NCLEX examination. You also have access to their final grade in university. The complete data are shown in the table below. Use these data to answer the questions below the table. Assume a 0.05 level of significance.

1. Use SPSS to obtain the predictive equation. Provide the equation and the supporting SPSS output. [1 Mark]

2. Use an appropriate statistic provided by the SPSS output to describe the utility (goodness) of the regression equation for predicting NCLEX scores. [1 Mark]

3. What is the predicted NCLEX score for a final grade = 75? [1 Mark]

4. What is the unexplained variation in NCLEX scores for your regression model? Show your calculation. [1 Mark]

A research service estimates that the mean annual consumption of fresh market tomatoes by a person in the US is atleast 21 pounds. You doubt this claim. A simple random sample of 23 people in the US has a mean annual consumption of fresh market tomatoes of Xbar=19 pounds and a standard deviation of 4 pounds. Assume the pop. is normally distributed. Construct the appropriate hypothesis and conduct the test at the 1% level of significance. Based on the Critical Value approach is there enough evidence to reject the claim?

A nutrition lab tested 40 randomly selected hot dogs to see if their mean sodium content was less than 325mg upper limit set by regulations for "reduced sodium" franks. The sample yielded a mean of 322 mg with a standard deviation of 11.5 mg.

A) To construct a confidence interval, would you use a z-chart or a t-chart? why?

B) Construct a 90% confidence interval for for estimating the mean sodium content for "reduced sodium" hot dogs. Interpret the confidence interval in a sentence.

C) Test the claim that the mean sodium level for the "reduced sodium" hot dogs is less than the limit of 325mg. Use a significance level of 0.05.

D) Does the confidence interval support the conclusion of the hypothesis test? Explain.

The density of an oil mixture (mix) as a function of the temperature (T) and the mass fraction of the three components (mi) was measured and results are shown :

T (K) m1 m2 m3 Pmix (kg/m3 )

300 0 1 0 879.6

320 0 0.5 0.5 870.6

340 0 0 1 863.6

360 0.5 0 0.5 846.4

380 0.5 0.25 0.25 830.8

400 0.5 0.5 0 819.1

420 1 0 0 796

440 1 0 0 778.2

Find the coefficients for a multiple regression of the form Pmix = a0 + a1*T + a2*m1 + a3*m2 + a4*m3