Homework Help for Statistics

 Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards.

Chapter 8 of independence sample t-test

1. A social work agency specializes in treating families in crisis. One of their goals is to increase the stability of the family, reducing the frequency of times of distress. The common practice in the agency is for a team of crisis counselors to respond in those times that families are in distress, hopefully helping them to learn healthier ways to cope with the challenges they face. A new director has arrived, and wants to test a new kind of intervention. For this intervention, the social work counselors will meet regularly with clients to educate them on stress and conflict management strategies, in addition to being available on an as needed basis. The director decides to test the new intervention, by assigning one group of families to be in the 'control' condition, and simply receive the usual assistance, and another group of families to be in the 'intervention' condition, who also receive the regularly scheduled stress and conflict management education. The director wants to know whether families who receive the intervention score better on a family stability test than families who do not receive the intervention.

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In preparation for the next school year, the school administrator wants to estimate the GWA. If they want to estimate the GWA accurate within an error of 0.75 from its true value, answer the following.

19. What is the estimated population standard deviation?
A.3.33  B.3.45  C.3.43  D.2.93  20. What should be the sample size at 99% confidence level? (2 points)
A.141  B.425  C.375  D.200  21. What should be the sample size at 95% confidence level? (2 points)
A.92  B.104  C.65  D.82

1. The data in “Cluster Analysis_Mobile phone survey.xls” contains several demographic variables as well as seven variables measuring attitudes towards mobile phones, where respondents were asked to give their degree of agreement/disagreement with the following statements:

• Technology is fascinating
• I am often surprised by the size of bills
• I find it difficult to determine the best deal
• I spent a lot of time shopping for the best deal
• I closely monitor the time I spend on the phone
• Cost is a factor when deciding where to SMS or phone
• I try to keep calls short and to the point

The scale used was:

Perform a Cluster Analysis on this dataset to see if the Mobile phone customers can be segmented into different market populations.  Create a summary of the unique aspects of each of the clusters.  Examine alternative cluster analysis solutions. Generally, it is helpful to explore solutions with fewer clusters than those automatically suggested.  Come up with evocative names for each group (e.g., "The big talkers").

Apply the concept of the Central Limit Theorem to answer the 
following.
Numbers 1 -3: Twenty (20) ABM students were selected at random from the respondents. 
Assuming that the population standard deviation of the GWA of ABM students is 3.3912. 
1. What is the probability that their mean GWA is above 86? (2 points)
A. 0.0005

B. 0.0143

C. 0.9861

D. 0.9995

2. What is the probability form that describes the probability of number 1?
A. P(X>86)

B. P(X<86)

C. P(𝑋̅>86)

D. P(X<86)

3. Which normal distribution best describes the probability of number 1

In preparation for the next school year, the school administrator wants to 
estimate the GWA. If they want to estimate the GWA accurate within an error of 0.75 from its true value,

19. What is the estimated population standard deviation?
      A. 2.93     B. 3.33      C. 3.43      D. 3.45
20. What should be the sample size at 99% confidence level? (2 points)
      A. 141      B. 200       C. 375        D. 425
21. What should be the sample size at 95% confidence level? (2 points)
      A. 65        B. 82         C. 92          D. 104

Fifty (50) STEM students were selected at random from the respondents.
7. What is the probability that their average grade is between 86 and 88? (2 points)
      A. 0.0001       B. 0.2235       C. 0.3014       D. 0.9999
8. What is the probability form that describes the probability of number 7?
      A. P(86<𝑋̅<88)       C. P(86<X<88)
      B. P(86>𝑋̅>88)       D. P(86>X>88)

 Ten (10) HUMSS students were selected from the respondents. Assuming 
that the population standard deviation of the GWA of HUMSS students is 3.6752. 
4. What is the probability that their average grade is below 88? (2 points)
      A. 0.3483         B. 0.409           C. 0.6064         D. 0.6517
5. What is the probability form that describes the probability of number 4?
      A. P(X<88)       B. P(X>88)       C. P(𝑋̅<88)       D. P(𝑋̅>88)

SECTION II

Green & Fast Motor (GFM) manufactures passenger cars. It equips its cars with Power tyres

supplied by the Power Drive Corporation (PDC), before delivering them to its two regional

distributors located in the East and West of the country. PDC's product information shows that

the lifespan of a Power tyre follows a Normal Distribution with mean value of 40000 kilometres

(km) and standard deviation of 2000 km.

Question 1

(a) GFM's management wants to understand more about the Power tyres.

(i) Find the distance that 80% of the Power tyres can last beyond.

(ii) The company's Data Analyst wants to take a sample of Power tyres to study their

performances. He took data from only 12 tyres as he is constrained by time and

resources for the analysis. Evaluate the probability that the mean lifespan of these

12 tyres will be at least 41000 km. Explain why the Analyst can use a small sample

size.

(b) Eco Earth Enterprise (EEE) has developed its new Eco tyre based on the latest synthetic

material. While promoting its tyre to SFM, EEE's Sales Director boasted that Eco tyre

provides better fuel efficiency (measured in km/litre) than Power tyre for vehicles.

GFM's management bought one shipment of Eco tyres. It equipped the cars for its East

Region distributor with Eco tyres while those for the West Region distributor continued

to use Power tyres. A sample of cars sold by each distribution is monitored and the cars'

fuel efficiencies are recorded as shown in the data file

(Fuel_Efficiencies_Eco_n_Power.xlsx).

FE with Power tyres FE with Eco tyres                                10.30                                 11.30                                 11.10                                 10.90                                 11.50                                 11.40                                    7.70                                 11.90                                 12.90                                 11.30                                 10.70                                 11.90                                    9.90                                    8.00                                 11.70                                 12.10                                    9.70                                 11.10                                 10.00                                 11.20                                 10.00                                    9.00                                    9.10                                 12.00                                 10.60                                    8.80                                    8.90                                 13.20                                    9.80                                    9.40                                 12.00                                 11.00                                 11.10                                    9.70                                 11.00                                 10.90                                 12.70                                 12.40                                    9.30                                 12.70                                  10.10                                 11.60                                 10.10                                 11.70                                    9.20                                    9.30                                 10.70                                    8.50                                 10.10                                   10.10       

Use Microsoft Excel to summarise separately the two (2) samples of data on the cars'

fuel efficiencies. Identify the locations and spreads of the samples, each with a measure

that takes all data into consideration. Comment on their differences.

Present the data in an appropriate type of diagram. Comment on the data distributions.

(c) Using the Excel summary output in Q1(b), identify the 95% Confidence Interval (CI)

estimate of the mean fuel efficiency for each type of tyre used and interpret this

confidence interval. Hence infer any differences in the fuel efficiencies provided by the

two (2) different tyres.

State the requirement in using t-distributions to construct the confidence intervals.

Justify whether this requirement is met in both cases.

Relating to above

(a) Develop an appropriate Hypothesis Test at 0.05 significant level to validate EEE's claim.

You must use the critical value approach, show the five (5) test steps and calculate the

test statistic by using data from the Excel Summary output from Question 1(b).

Examine and explain the type of Hypothesis Test Error that may occur in this analysis

and the consequence of this error.

(b) Apply Microsoft Excel to conduct the same test as Q2(a) but at 0.10 significant level,

using p value approach. You only need to show the steps which are different from the

test in Q2(a) and make your test conclusion based on the p value obtained from the Excel

test output.

(c) GFM consults you on the Statistic and Test procedures conducted. Discuss two (2)

shortcomings (excludes the issue on type of Test Error in Question 2(a) and how you would have done differently to obtain more robust test results).

An Analysis of the fall and introduction of sin into history and creation

Dataset: 37, 25, 40, 49, 26, 33, 59, 21

μx = 51

1. What is the variance?
2. What is the mean?
3. When calculating the t-value, what is the numerator, denominator, and the final t-value?
4. Degrees of freedom
5. Critical value. Do you use one tail or two tail? Why?
6. Would you reject the null hypothesis?

Use 4 decimals for the answers.

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I did the work but not sure if my answers are correct. Please let me know if the answers are good. If your results do not coincide with mine, please let me know how you did it. Thanks so much

Mean=36.25. Sum of squares is 1169.5. Variance is 146.1875. df = 7, used two tail. t numerator is -14.75, denominator is 4.5699, t = -3.2276.

Critical value is +- 2.365

i should reject because t < -2.365

What is role of randomization in experiments mcq question on R programming?

The precision of a method is being established, and the following data are obtained: 22.23.22.18, 22.25, 22.09, and 22.17%. Is 22.09% a valid measurement at the 95% confidence level?

The following replicate molarities were obtained when standardizing a solution: 0.1067, 0.1071, 0.1066, and 0.1050. Can one of the results be discarded as due to accidental error at the 95%confidence level?

1. A study is being performed to see if there is a correlation between the concentration of chromium in the blood and a suspected disease. Blood samples from a series of volunteers with a history of the disease and other indicators of susceptibility are analyzed and compared with the results from the analysis of samples from healthy control subjects. From the following results, determine whether the differences between the 12, 18, 9, 28, 11, 10. Disease group: 25, 20, 35, 32, 15, 40,16, 10, 22, 18.